zbMATH — the first resource for mathematics

Krishnaiah, Paruchuri Rama

Compute Distance To:
 Author ID: krishnaiah.paruchuri-r Published as: Krishnaiah, P. R.; Krishnaiah, Paruchuri R. External Links: MGP · Math-Net.Ru · dblp · GND
 Documents Indexed: 150 Publications since 1961, including 41 Books Biographic References: 3 Publications
all top 5

Co-Authors

 28 single-authored 18 Bai, Zhi-Dong 15 Schuurmann, Frederick J. 11 Zhao, Lincheng 10 Yin, Y.-Q. 9 Lee, Jack Chao-Sheng 7 Waikar, Vasant B. 6 Sen, Pranab Kumar 5 Chen, Xiru 4 Rao, Calyampudi Radhakrishna 3 Fujikoshi, Yasunori 3 Kariya, Takeaki 3 Liang, Wenqi 3 Rizvi, M. Haseeb 3 Sarkar, Shakuntala 2 Armitage, John Vernon 2 Breiter, M. C. 2 Gupta, Arjun Kumar 2 Kanal, Laveen N. 2 Miao, Bai-qi 2 Nagarsenker, Brahmanand N. 2 Nishii, Ryuei 2 Pathak, Pramod K. 2 Pukkila, Tarmo Mikko 2 Rao, Malempati M. 2 Steinberg, Leon 1 Bhaskara Rao, M. 1 Brillinger, David R. 1 Clemm, D. S. 1 Cox, C. M. 1 Ghosh, Jayanta Kumar 1 Hagis, Peter jun. 1 Hannan, Edward James 1 Kallianpur, Gopinath 1 Kaskey, G. 1 Kolman, Bernard 1 Lin, Jugan 1 Mudholkar, Govind S. 1 Reising, J. 1 Sambamoorthi, N. 1 Schmidhammer, James L. 1 Sinha, Bimal Kumar 1 Subbaiah, Perla 1 Subramanyam, Kasala 1 Yochmowitz, Michael G.
all top 5

Serials

 18 Journal of Multivariate Analysis 11 Annals of the Institute of Statistical Mathematics 9 Handbook of Statistics 5 Teoriya Veroyatnosteĭ i eë Primeneniya 5 Sankhyā. Series A. Methods and Techniques 4 Theory of Probability and its Applications 3 Sankhyā. Series B. Methodological 3 South African Statistical Journal 3 Communications in Statistics. Theory and Methods 3 Journal of Statistical Computation and Simulation 3 Annals of Mathematical Statistics 2 The Australian Journal of Statistics 2 IEEE Transactions on Acoustics, Speech, and Signal Processing 2 Communications in Statistics 1 American Mathematical Monthly 1 IEEE Transactions on Information Theory 1 Econometrica 1 Hiroshima Mathematical Journal 1 Journal of Statistical Planning and Inference 1 Technometrics 1 Chinese Annals of Mathematics. Series B 1 Acta Mathematicae Applicatae Sinica. English Series 1 Probability Theory and Related Fields 1 Journal of China University of Science and Technology 1 Mathematical and Computer Modelling 1 Communications in Statistics. Simulation and Computation 1 SIAM Review
all top 5

Fields

 136 Statistics (62-XX) 17 General and overarching topics; collections (00-XX) 14 Probability theory and stochastic processes (60-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 3 Approximations and expansions (41-XX) 3 Information and communication theory, circuits (94-XX) 2 Special functions (33-XX) 2 Numerical analysis (65-XX) 1 Ordinary differential equations (34-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 Computer science (68-XX) 1 Systems theory; control (93-XX)

Citations contained in zbMATH Open

108 Publications have been cited 663 times in 476 Documents Cited by Year
On the limit of the largest eigenvalue of the large dimensional sample covariance matrix. Zbl 0627.62022
Yin, Y. Q.; Bai, Z. D.; Krishnaiah, P. R.
1988
On detection of the number of signals in presence of white noise. Zbl 0617.62055
Zhao, L. C.; Krishnaiah, P. R.; Bai, Z. D.
1986
Remarks on a multivariate gamma distribution. Zbl 0131.17303
Krishnaiah, P. R.; Rao, M. M.
1961
Asymptotic distributions of functions of the eigenvalues of some random matrices for nonnormal populations. Zbl 0497.62025
Fang, C.; Krishnaiah, P. R.
1982
A limit theorem for the eigenvalues of product of two random matrices. Zbl 0553.62018
Yin, Y. Q.; Krishnaiah, P. R.
1983
A note on the bivariate chi distribution. Zbl 0115.36903
Krishnaiah, P. R.; Hagis, Peter jun.; Steinberg, Leon
1963
On the exact distributions of the extreme roots of the Wishart and MANOVA matrices. Zbl 0224.62022
Krishnaiah, P. R.; Chang, T. C.
1971
Some recent developments on complex multivariate distributions. Zbl 0358.62040
Krishnaiah, P. R.
1976
On detection of the number of signals when the noise covariance matrix is arbitrary. Zbl 0617.62056
Zhao, L. C.; Krishnaiah, P. R.; Bai, Z. D.
1986
On rates of convergence of efficient detection criteria in signal processing with white noise. Zbl 0677.94001
Bai, Zhi-Dong; Krishnaiah, Paruchuri R.; Zhao, Lin-Cheng
1989
On the distributions of the ratios of the extreme roots to the trace of the Wishart matrix. Zbl 0286.62031
Schuurmann, F. J.; Krishnaiah, P. R.; Chattopadhyay, A. K.
1973
On the evaluation of some distributions that arise in simultaneous tests for the equality of the latent roots of the covariance matrix. Zbl 0309.62032
Krishnaiah, P. R.; Schuurmann, F. J.
1974
Computations of some multivariate distributions. Zbl 0456.62041
Krishnaiah, P. R.
1980
Limiting behavior of the eigenvalues of a multivariate F matrix. Zbl 0531.62018
Yin, Y. Q.; Bai, Z. D.; Krishnaiah, P. R.
1983
A note on the joint distribution of correlated quadratic forms. Zbl 0379.62037
Khatri, C. G.; Krishnaiah, P. R.; Sen, P. K.
1977
On the asymptotic joint distributions of certain functions of the eigenvalues of four random matrices. Zbl 0408.62043
Krishnaiah, P. R.; Lee, Jack C.
1979
On the simultaneous ANOVA and MANOVA tests. Zbl 0138.14401
Krishnaiah, P. R.
1965
Simultaneous tests for equality of latent roots against certain alternatives. II. Zbl 0327.62036
Krishnaiah, P. R.; Waikar, V. B.
1972
On the limiting empirical distribution function of the eigenvalues of a multivariate F matrix. Zbl 0676.62021
Bai, Z. D.; Yin, Y. Q.; Krishnaiah, P. R.
1987
Simultaneous tests for equality of latent roots against certain alternatives. I. Zbl 0256.62046
Krishnaiah, P. R.; Waikar, V. B.
1971
On some noncentral distributions in multivariate analysis. Zbl 0345.62037
Krishnaiah, P. R.; Chattopadhyay, A. K.
1975
Some recent developments on real multivariate distributions. Zbl 0415.62035
Krishnaiah, P. R.
1978
Inference on the structure of interaction in two-way classification model. Zbl 0462.62054
Krishnaiah, P. R.; Yochmowitz, M. G.
1980
On limiting spectral distribution of product of two random matrices when the underlying distribution is isotropic. Zbl 0657.62058
Bai, Z. D.; Yin, Y. Q.; Krishnaiah, P. R.
1986
Strong consistency of the information criterion for model selection in multivariate analysis. Zbl 0678.62064
Nishii, Ryuei; Bai, Zhidong; Krishnaiah, Paruchuri R.
1988
Exact joint distributions of any few ordered roots of a class of random matrices. Zbl 0224.62021
Krishnaiah, P. R.; Waikar, V. B.
1971
On the exact distribution of the smallest root of the Wishart matrix using zonal polynomials. Zbl 0276.62053
Krishnaiah, P. R.; Chang, T. C.
1971
Some developments on simultaneous test procedures. Zbl 0464.62044
Krishnaiah, P. R.
1979
Test for independence of two multivariate regression equations with different design matrices. Zbl 0558.62047
Kariya, Takeaki; Fujikoshi, Yasunori; Krishnaiah, P. R.
1984
Limit theorem for the eigenvalues of the sample covariance matrix when the underlying distribution is isotropic. Zbl 0658.62025
Yin, Y. Q.; Krishnaiah, P. R.
1986
A note on moments of gamma order statistics. Zbl 0147.18806
Krishnaiah, P. R.; Rizvi, M. H.
1967
Complex elliptically symmetric distributions. Zbl 0607.62052
Krishnaiah, P. R.; Lin, Jugan
1986
On the exact distributions of the traces of $$S_1(S_1+S_2)^{-1}$$ and $$S_1S_2^{-1}$$. Zbl 0263.62033
Krishnaiah, P. R.; Chang, T. C.
1972
Inference on parameters of multivariate normal populations when some data is missing. Zbl 0559.62042
Kariya, T.; Krishnaiah, P. R.; Rao, C. R.
1983
On limiting empirical distribution function of the eigenvalues of a multivariate F matrix. Zbl 0635.62018
Bai, Z. D.; Yin, Y. Q.; Krishnaiah, P. R.
1987
On the moments of classical estimates of explanatory variables under a multivariate calibration model. Zbl 0645.62070
Nishii, R.; Krishnaiah, P. R.
1988
Asymptotic distributions of the determinants of some random matrices. Zbl 0296.62038
Gupta, A. K.; Chattopadhyay, A. K.; Krishnaiah, P. R.
1975
Almost sure $$L_ r$$-norm convergence for data-based histogram density estimates. Zbl 0721.62037
Zhao, L. C.; Krishnaiah, P. R.; Chen, X. R.
1990
Asymptotic distributions of the likelihood ratio test statistics for covariance structures of the complex multivariate normal distributions. Zbl 0496.62018
Fang, C.; Krishnaiah, P. R.; Nagarsenker, B. N.
1982
Developments in statistics. Vol. 1. Zbl 0406.00020
Krishnaiah, Paruchuri R. (ed.)
1978
A structure theorem on bivariate positive quadrant dependent distributions and tests for independence in two-way contingency tables. Zbl 0627.62056
Bhaskara Rao, M.; Krishnaiah, P. R.; Subramanyam, K.
1987
Tables for the moments of gamma order statistics. Zbl 0164.18808
Breiter, M. C.; Krishnaiah, P. R.
1967
Tests for the equality of covariance matrices under the intraclass correlation model. Zbl 0166.15201
Krishnaiah, P. R.; Pathak, P. K.
1968
Limit theorem for the eigenvalues of the sample covariance matrix when the underlying distribution is isotropic. Zbl 0584.62029
Yin, Y. Q.; Krishnaiah, P. R.
1985
Tests for the equality of the covariance matrices of correlated multivariate normal populations. Zbl 0264.62018
Krishnaiah, P. R.
1973
Tables for the extreme roots of the Wishart matrix. Zbl 0283.62102
Clemm, D. S.; Krishnaiah, P. R.; Waikar, V. B.
1973
Likelihood ratio tests for mean vectors and covariance matrices. Zbl 0469.62040
Krishnaiah, P. R.; Lee, Jack C.
1980
Asymptotic joint distributions of functions of the elements of sample covariance matrix. Zbl 0486.62049
Fang, C.; Krishnaiah, P. R.
1982
Time series in the frequency domain. Zbl 0527.00026
Brillinger, D. R. (ed.); Krishnaiah, P. R. (ed.)
1983
On a class of simultaneous rank order tests in MANOCOVA. Zbl 0337.62051
Sen, P. K.; Krishnaiah, P. R.
1974
On covariance structures. Zbl 0412.62032
Krishnaiah, P. R.; Lee, Jack C.
1976
On the use of autoregressive order determination criteria in univariate white noise tests. Zbl 0647.62083
Pukkila, Tarmo M.; Krishnaiah, Paruchuri R.
1988
Effect of additional variables in principal component analysis, discriminant analysis and canonical correlation analysis. Zbl 0652.62051
Fujikoshi, Y.; Krishnaiah, P. R.; Schmidhammer, J.
1987
On the use of autoregressive order determination criteria in multivariate white noise tests. Zbl 0656.62099
Pukkila, Tarmo M.; Krishnaiah, Paruchuri R.
1988
A note on recurrence relations between expected values of functions of order statistics. Zbl 0138.13904
Krishnaiah, P. R.; Rizvi, M. H.
1966
Multiple comparison tests in multi-response experiments. Zbl 0138.14403
Krishnaiah, P. R.
1965
Simultaneous tests for the equality of covariance matrices against certain alternatives. Zbl 0162.50205
Krishnaiah, P. R.
1968
Time series in the time domain. Zbl 0578.62074
Hannan, E. J. (ed.); Krishnaiah, P. R. (ed.); Rao, M. M. (ed.)
1985
On tests for selection of variables and independence under multivariate regression models. Zbl 0614.62065
Kariya, T.; Fujikoshi, Y.; Krishnaiah, P. R.
1987
Approximations to the distributions of the likelihood ratio statistics for testing certain structures on the covariance matrices of real multivariate normal populations. Zbl 0313.62036
Lee, J. C.; Chang, T. C.; Krishnaiah, P. R.
1975
Percentage points of the joint distribution of the extreme roots of the random matrix $$S_1(S_1+S_2)^{-1}$$. Zbl 0282.62090
Schuurmann, F. J.; Waikar, V. B.; Krishnaiah, P. R.
1973
On the exact distributions of the individual roots of the complex Wishart and multivariate beta matrices. Zbl 0291.62154
Krishnaiah, P. R.; Schuurmann, F. J.
1974
Asymptotic distributions of functions of the eigenvalues of the real and complex noncentral Wishart matrices. Zbl 0482.62043
Fang, C.; Krishnaiah, P. R.
1981
Classification, pattern recognition and reduction of dimensionality. Zbl 0496.00013
Krishnaiah, P. R. (ed.); Kanal, L. N. (ed.)
1982
Selection of variables in discriminant analysis. Zbl 0506.62047
Krishnaiah, P. R.
1982
Model selection for log-linear models. Zbl 0764.62048
Bai, Z. D.; Krishnaiah, P. R.; Sambamoorthi, N.; Zhao, L. C.
1992
Nonparametric iterative estimation of multivariate binary density. Zbl 0558.62034
Liang, Wen-Qi; Krishnaiah, P. R.
1985
Reconstruction of the shape and size of objects from two orthogonal projections. Zbl 0683.52003
Bai, Z. D.; Krishnaiah, P. R.; Rao, C. R.; Sun, Y. N.; Zhao, L. C.
1989
Nonparametric methods. Zbl 0587.00012
Krishnaiah, P. R. (ed.); Sen, P. K. (ed.)
1984
A note on confidence bounds for certain ratios of characteristic roots of co-variance matrices. Zbl 0177.46404
Krishnaiah, P. R.; Pathak, P. K.
1968
On a multivariate F distribution. Zbl 0225.62141
Krishnaiah, P. R.; Armitage, J. V.
1970
Tables for the distributions of the ratios of the extreme roots to the trace of Wishart matrix. Zbl 0257.62061
Schuurmann, F. J.; Krishnaiah, P. R.; Chattopadhyay, A. K.
1973
On the distributions of the ratios of the extreme roots of the real and complex multivariate beta matrices. Zbl 0297.62030
Krishnaiah, P. R.; Schuurmann, F. J.
1974
Developments in statistics. Vol. 2. Zbl 0453.00035
Krishnaiah, Paruchuri R. (ed.)
1979
Statistics and probability: Essays in Honor of C. R. Rao. Zbl 0474.00011
Kallianpur, Gopinath (ed.); Krishnaiah, P. R. (ed.); Ghosh, J. K. (ed.)
1982
Variable selection in logistic regression. Zbl 0741.62057
Bai, Zhidong; Krishnaiah, P. R.
1991
Sampling. Zbl 0662.62006
Krishnaiah, P. R. (ed.); Rao, C. R. (ed.)
1988
Quality control and reliability. Zbl 0673.62089
Krishnaiah, P. R. (ed.); Rao, C. R. (ed.)
1988
On the distribution of the likelihood ratio test statistic for compound symmetry. Zbl 0338.62029
Lee, Jack C.; Krishnaiah, P. R.; Chang, T. C.
1976
Multivariate analysis - IV. Proceedings of the 4th international symposium on multivariate analysis. Zbl 0348.00011
Krishnaiah, Paruchuri R. (ed.)
1977
Tables for a multivariate F distribution. Zbl 0352.62090
Schuurmann, F. J.; Krishnaiah, P. R.; Chattopadhyay, A. K.
1975
Approximations to the distributions of the determinants of real and complex multivariate beta matrices. Zbl 0369.62057
Lee, Jack C.; Krishnaiah, P. R.; Chang, T. C.
1977
Approximations to the distributions of the likelihood ratio statistics for testing the hypotheses on covariance matrices and mean vectors simultaneously. Zbl 0373.62032
Chang, T. C.; Krishnaiah, P. R.; Lee, J. C.
1977
A study on finite intersection tests for multiple comparisons of means. Zbl 0434.62054
Cox, C. M.; Krishnaiah, P. R.; Lee, J. C.; Reising, J.; Schuurmann, F. J.
1980
On the asymptotic distributions of certain functions of eigenvalues of correlation matrices. Zbl 0461.62047
Lee, Jack C.; Krishnaiah, P. R.
1980
Tests for sphericity under correlated multivariate regression equations model. Zbl 0622.62020
Sarkar, Shakuntala; Krishnaiah, P. R.
1987
Estimation of multivariate binary density using orthogonal functions. Zbl 0687.62040
Chen, X. R.; Krishnaiah, P. R.; Liang, W. W.
1989
On asymptotic joint distribution of the eigenvalues of the noncentral MANOVA matrix for nonnormal populations. Zbl 0627.62021
Bai, Z. D.; Krishnaiah, P. R.; Liang, W. Q.
1986
Principal component analysis under correlated multivariate regression equations model. Zbl 0649.62052
Krishnaiah, P. R.; Sarkar, Shakuntala
1987
Strong consistency of maximum likelihood parameter estimation of superimposed exponential signals in noise. Zbl 0776.62023
Bai, Z. D.; Chen, X. R.; Krishnaiah, P. R.; Wu, Y. H.; Zhao, L. G.
1991
On a multivariate generalization of the simultaneous analysis of variance test. Zbl 0134.36502
Krishnaiah, P. R.
1965
Simultaneous tests for trend and serial correlations for Gaussian Markov residuals. Zbl 0143.41203
Krishnaiah, P. R.; Murthy, V. K.
1966
Nonparametric estimation of multivariate density using Laguerre and Hermite polynomials. Zbl 0583.62033
Krishnaiah, P. R.; Sarkar, Shakuntala
1985
Limit theorems for the eigenvalues of product of large dimensional random matrices when the underlying distribution is isotropic. Zbl 0605.62013
Yin, Y. Q.; Krishnaiah, P. R.
1986
Approximations to the distributions of the determinants of real and complex multivariate beta matrices. Zbl 0314.62051
Lee, J. C.; Krishnaiah, P. R.; Chang, T. C.
1975
Multivariate analysis. Proceedings of an international symposium held in Dayton, Ohio, June 14–19, 1965. Zbl 0209.21401
Krishnaiah, Paruchuri R. (ed.)
1966
Some asymptotic simultaneous tests for multivariate moving average processes. Zbl 0212.50603
Krishnaiah, P. R.; Sen, P. K.
1971
On the exact distributions of the traces of $$S_1(S_1+S_2)^{-1}$$ and $$S_1S_2^{-1}$$. Zbl 0236.62039
Krishnaiah, P. R.; Chang, T. C.
1970
Exact distributions of a few arbitrary roots of some complex random matrices. Zbl 0245.62053
Waikar, V. B.; Chang, T. C.; Krishnaiah, P. R.
1972
Tables for the probability integrals of the bivariate $$t$$ distribution. Zbl 0249.65002
Krishnaiah, P. R.; Armitage, J. V.; Breiter, M. C.
1969
Model selection for log-linear models. Zbl 0764.62048
Bai, Z. D.; Krishnaiah, P. R.; Sambamoorthi, N.; Zhao, L. C.
1992
Variable selection in logistic regression. Zbl 0741.62057
Bai, Zhidong; Krishnaiah, P. R.
1991
Strong consistency of maximum likelihood parameter estimation of superimposed exponential signals in noise. Zbl 0776.62023
Bai, Z. D.; Chen, X. R.; Krishnaiah, P. R.; Wu, Y. H.; Zhao, L. G.
1991
Almost sure $$L_ r$$-norm convergence for data-based histogram density estimates. Zbl 0721.62037
Zhao, L. C.; Krishnaiah, P. R.; Chen, X. R.
1990
On rates of convergence of efficient detection criteria in signal processing with white noise. Zbl 0677.94001
Bai, Zhi-Dong; Krishnaiah, Paruchuri R.; Zhao, Lin-Cheng
1989
Reconstruction of the shape and size of objects from two orthogonal projections. Zbl 0683.52003
Bai, Z. D.; Krishnaiah, P. R.; Rao, C. R.; Sun, Y. N.; Zhao, L. C.
1989
Estimation of multivariate binary density using orthogonal functions. Zbl 0687.62040
Chen, X. R.; Krishnaiah, P. R.; Liang, W. W.
1989
Normalizing transformations of some statistics of Gaussian ARMA processes. Zbl 0693.62073
Taniguchi, M.; Krishnaiah, P. R.; Chao, R.
1989
On the limit of the largest eigenvalue of the large dimensional sample covariance matrix. Zbl 0627.62022
Yin, Y. Q.; Bai, Z. D.; Krishnaiah, P. R.
1988
Strong consistency of the information criterion for model selection in multivariate analysis. Zbl 0678.62064
Nishii, Ryuei; Bai, Zhidong; Krishnaiah, Paruchuri R.
1988
On the moments of classical estimates of explanatory variables under a multivariate calibration model. Zbl 0645.62070
Nishii, R.; Krishnaiah, P. R.
1988
On the use of autoregressive order determination criteria in univariate white noise tests. Zbl 0647.62083
Pukkila, Tarmo M.; Krishnaiah, Paruchuri R.
1988
On the use of autoregressive order determination criteria in multivariate white noise tests. Zbl 0656.62099
Pukkila, Tarmo M.; Krishnaiah, Paruchuri R.
1988
Sampling. Zbl 0662.62006
Krishnaiah, P. R.; Rao, C. R.
1988
Quality control and reliability. Zbl 0673.62089
Krishnaiah, P. R.; Rao, C. R.
1988
On the limiting empirical distribution function of the eigenvalues of a multivariate F matrix. Zbl 0676.62021
Bai, Z. D.; Yin, Y. Q.; Krishnaiah, P. R.
1987
On limiting empirical distribution function of the eigenvalues of a multivariate F matrix. Zbl 0635.62018
Bai, Z. D.; Yin, Y. Q.; Krishnaiah, P. R.
1987
A structure theorem on bivariate positive quadrant dependent distributions and tests for independence in two-way contingency tables. Zbl 0627.62056
Bhaskara Rao, M.; Krishnaiah, P. R.; Subramanyam, K.
1987
Effect of additional variables in principal component analysis, discriminant analysis and canonical correlation analysis. Zbl 0652.62051
Fujikoshi, Y.; Krishnaiah, P. R.; Schmidhammer, J.
1987
On tests for selection of variables and independence under multivariate regression models. Zbl 0614.62065
Kariya, T.; Fujikoshi, Y.; Krishnaiah, P. R.
1987
Tests for sphericity under correlated multivariate regression equations model. Zbl 0622.62020
Sarkar, Shakuntala; Krishnaiah, P. R.
1987
Principal component analysis under correlated multivariate regression equations model. Zbl 0649.62052
Krishnaiah, P. R.; Sarkar, Shakuntala
1987
On detection of the number of signals in presence of white noise. Zbl 0617.62055
Zhao, L. C.; Krishnaiah, P. R.; Bai, Z. D.
1986
On detection of the number of signals when the noise covariance matrix is arbitrary. Zbl 0617.62056
Zhao, L. C.; Krishnaiah, P. R.; Bai, Z. D.
1986
On limiting spectral distribution of product of two random matrices when the underlying distribution is isotropic. Zbl 0657.62058
Bai, Z. D.; Yin, Y. Q.; Krishnaiah, P. R.
1986
Limit theorem for the eigenvalues of the sample covariance matrix when the underlying distribution is isotropic. Zbl 0658.62025
Yin, Y. Q.; Krishnaiah, P. R.
1986
Complex elliptically symmetric distributions. Zbl 0607.62052
Krishnaiah, P. R.; Lin, Jugan
1986
On asymptotic joint distribution of the eigenvalues of the noncentral MANOVA matrix for nonnormal populations. Zbl 0627.62021
Bai, Z. D.; Krishnaiah, P. R.; Liang, W. Q.
1986
Limit theorems for the eigenvalues of product of large dimensional random matrices when the underlying distribution is isotropic. Zbl 0605.62013
Yin, Y. Q.; Krishnaiah, P. R.
1986
Limit theorem for the eigenvalues of the sample covariance matrix when the underlying distribution is isotropic. Zbl 0584.62029
Yin, Y. Q.; Krishnaiah, P. R.
1985
Time series in the time domain. Zbl 0578.62074
Hannan, E. J.; Krishnaiah, P. R.; Rao, M. M.
1985
Nonparametric iterative estimation of multivariate binary density. Zbl 0558.62034
Liang, Wen-Qi; Krishnaiah, P. R.
1985
Nonparametric estimation of multivariate density using Laguerre and Hermite polynomials. Zbl 0583.62033
Krishnaiah, P. R.; Sarkar, Shakuntala
1985
Test for independence of two multivariate regression equations with different design matrices. Zbl 0558.62047
Kariya, Takeaki; Fujikoshi, Yasunori; Krishnaiah, P. R.
1984
Nonparametric methods. Zbl 0587.00012
Krishnaiah, P. R.; Sen, P. K.
1984
A limit theorem for the eigenvalues of product of two random matrices. Zbl 0553.62018
Yin, Y. Q.; Krishnaiah, P. R.
1983
Limiting behavior of the eigenvalues of a multivariate F matrix. Zbl 0531.62018
Yin, Y. Q.; Bai, Z. D.; Krishnaiah, P. R.
1983
Inference on parameters of multivariate normal populations when some data is missing. Zbl 0559.62042
Kariya, T.; Krishnaiah, P. R.; Rao, C. R.
1983
Time series in the frequency domain. Zbl 0527.00026
Brillinger, D. R.; Krishnaiah, P. R.
1983
Asymptotic distributions of functions of the eigenvalues of some random matrices for nonnormal populations. Zbl 0497.62025
Fang, C.; Krishnaiah, P. R.
1982
Asymptotic distributions of the likelihood ratio test statistics for covariance structures of the complex multivariate normal distributions. Zbl 0496.62018
Fang, C.; Krishnaiah, P. R.; Nagarsenker, B. N.
1982
Asymptotic joint distributions of functions of the elements of sample covariance matrix. Zbl 0486.62049
Fang, C.; Krishnaiah, P. R.
1982
Classification, pattern recognition and reduction of dimensionality. Zbl 0496.00013
Krishnaiah, P. R.; Kanal, L. N.
1982
Selection of variables in discriminant analysis. Zbl 0506.62047
Krishnaiah, P. R.
1982
Statistics and probability: Essays in Honor of C. R. Rao. Zbl 0474.00011
Kallianpur, Gopinath; Krishnaiah, P. R.; Ghosh, J. K.
1982
Asymptotic distributions of functions of the eigenvalues of the real and complex noncentral Wishart matrices. Zbl 0482.62043
Fang, C.; Krishnaiah, P. R.
1981
Computations of some multivariate distributions. Zbl 0456.62041
Krishnaiah, P. R.
1980
Inference on the structure of interaction in two-way classification model. Zbl 0462.62054
Krishnaiah, P. R.; Yochmowitz, M. G.
1980
Likelihood ratio tests for mean vectors and covariance matrices. Zbl 0469.62040
Krishnaiah, P. R.; Lee, Jack C.
1980
A study on finite intersection tests for multiple comparisons of means. Zbl 0434.62054
Cox, C. M.; Krishnaiah, P. R.; Lee, J. C.; Reising, J.; Schuurmann, F. J.
1980
On the asymptotic distributions of certain functions of eigenvalues of correlation matrices. Zbl 0461.62047
Lee, Jack C.; Krishnaiah, P. R.
1980
On the asymptotic joint distributions of certain functions of the eigenvalues of four random matrices. Zbl 0408.62043
Krishnaiah, P. R.; Lee, Jack C.
1979
Some developments on simultaneous test procedures. Zbl 0464.62044
Krishnaiah, P. R.
1979
Developments in statistics. Vol. 2. Zbl 0453.00035
Krishnaiah, Paruchuri R.
1979
Some recent developments on real multivariate distributions. Zbl 0415.62035
Krishnaiah, P. R.
1978
Developments in statistics. Vol. 1. Zbl 0406.00020
Krishnaiah, Paruchuri R.
1978
A note on the joint distribution of correlated quadratic forms. Zbl 0379.62037
Khatri, C. G.; Krishnaiah, P. R.; Sen, P. K.
1977
Multivariate analysis - IV. Proceedings of the 4th international symposium on multivariate analysis. Zbl 0348.00011
Krishnaiah, Paruchuri R.
1977
Approximations to the distributions of the determinants of real and complex multivariate beta matrices. Zbl 0369.62057
Lee, Jack C.; Krishnaiah, P. R.; Chang, T. C.
1977
Approximations to the distributions of the likelihood ratio statistics for testing the hypotheses on covariance matrices and mean vectors simultaneously. Zbl 0373.62032
Chang, T. C.; Krishnaiah, P. R.; Lee, J. C.
1977
Some recent developments on complex multivariate distributions. Zbl 0358.62040
Krishnaiah, P. R.
1976
On covariance structures. Zbl 0412.62032
Krishnaiah, P. R.; Lee, Jack C.
1976
On the distribution of the likelihood ratio test statistic for compound symmetry. Zbl 0338.62029
Lee, Jack C.; Krishnaiah, P. R.; Chang, T. C.
1976
On some noncentral distributions in multivariate analysis. Zbl 0345.62037
Krishnaiah, P. R.; Chattopadhyay, A. K.
1975
Asymptotic distributions of the determinants of some random matrices. Zbl 0296.62038
Gupta, A. K.; Chattopadhyay, A. K.; Krishnaiah, P. R.
1975
Approximations to the distributions of the likelihood ratio statistics for testing certain structures on the covariance matrices of real multivariate normal populations. Zbl 0313.62036
Lee, J. C.; Chang, T. C.; Krishnaiah, P. R.
1975
Tables for a multivariate F distribution. Zbl 0352.62090
Schuurmann, F. J.; Krishnaiah, P. R.; Chattopadhyay, A. K.
1975
Approximations to the distributions of the determinants of real and complex multivariate beta matrices. Zbl 0314.62051
Lee, J. C.; Krishnaiah, P. R.; Chang, T. C.
1975
Exact percentage points of the distribution of the trace of a multivariate beta matrix. Zbl 0309.62084
Schuurmann, F. J.; Krishnaiah, P. R.; Chattopadhyay, A. K.
1975
On the evaluation of some distributions that arise in simultaneous tests for the equality of the latent roots of the covariance matrix. Zbl 0309.62032
Krishnaiah, P. R.; Schuurmann, F. J.
1974
On a class of simultaneous rank order tests in MANOCOVA. Zbl 0337.62051
Sen, P. K.; Krishnaiah, P. R.
1974
On the exact distributions of the individual roots of the complex Wishart and multivariate beta matrices. Zbl 0291.62154
Krishnaiah, P. R.; Schuurmann, F. J.
1974
On the distributions of the ratios of the extreme roots of the real and complex multivariate beta matrices. Zbl 0297.62030
Krishnaiah, P. R.; Schuurmann, F. J.
1974
On the exact joint distributions of the extreme roots of the complex Wishart and multivariate beta matrices. Zbl 0291.62155
Krishnaiah, P. R.; Schuurmann, F. J.
1974
Approximations to the distributions of the traces of complex multivariate beta and F matrices. Zbl 0297.62031
Krishnaiah, P. R.; Schuurmann, F. J.
1974
On he exact distribution of the trace of a complex multivariate beta matrix. Zbl 0309.62031
Krishnaiah, P. R.; Schuurmann, F. J.
1974
On the distributions of the ratios of the extreme roots to the trace of the Wishart matrix. Zbl 0286.62031
Schuurmann, F. J.; Krishnaiah, P. R.; Chattopadhyay, A. K.
1973
Tests for the equality of the covariance matrices of correlated multivariate normal populations. Zbl 0264.62018
Krishnaiah, P. R.
1973
Tables for the extreme roots of the Wishart matrix. Zbl 0283.62102
Clemm, D. S.; Krishnaiah, P. R.; Waikar, V. B.
1973
Percentage points of the joint distribution of the extreme roots of the random matrix $$S_1(S_1+S_2)^{-1}$$. Zbl 0282.62090
Schuurmann, F. J.; Waikar, V. B.; Krishnaiah, P. R.
1973
Tables for the distributions of the ratios of the extreme roots to the trace of Wishart matrix. Zbl 0257.62061
Schuurmann, F. J.; Krishnaiah, P. R.; Chattopadhyay, A. K.
1973
Exact percentage points of the distribution of the trace of S$$_1$$ (S$$_1$$+S$$_2$$)-1. Zbl 0257.62039
Schuurmann, F. J.; Krishnaiah, P. R.; Chattopadhyay, A. K.
1973
On the distribution of a linear combination of correlated quadratic forms. Zbl 0261.62013
Krishnaiah, P. R.; Waikar, V. B.
1973
On the exact distributions of the test statistics based on the eigenvalues of complex random matrices. Zbl 0289.62034
Krishnaiah, P. R.
1973
Simultaneous tests for equality of latent roots against certain alternatives. II. Zbl 0327.62036
Krishnaiah, P. R.; Waikar, V. B.
1972
On the exact distributions of the traces of $$S_1(S_1+S_2)^{-1}$$ and $$S_1S_2^{-1}$$. Zbl 0263.62033
Krishnaiah, P. R.; Chang, T. C.
1972
Exact distributions of a few arbitrary roots of some complex random matrices. Zbl 0245.62053
Waikar, V. B.; Chang, T. C.; Krishnaiah, P. R.
1972
On the exact distributions of the extreme roots of the Wishart and MANOVA matrices. Zbl 0224.62022
Krishnaiah, P. R.; Chang, T. C.
1971
Simultaneous tests for equality of latent roots against certain alternatives. I. Zbl 0256.62046
Krishnaiah, P. R.; Waikar, V. B.
1971
Exact joint distributions of any few ordered roots of a class of random matrices. Zbl 0224.62021
Krishnaiah, P. R.; Waikar, V. B.
1971
On the exact distribution of the smallest root of the Wishart matrix using zonal polynomials. Zbl 0276.62053
Krishnaiah, P. R.; Chang, T. C.
1971
Some asymptotic simultaneous tests for multivariate moving average processes. Zbl 0212.50603
Krishnaiah, P. R.; Sen, P. K.
1971
On a multivariate F distribution. Zbl 0225.62141
Krishnaiah, P. R.; Armitage, J. V.
1970
On the exact distributions of the traces of $$S_1(S_1+S_2)^{-1}$$ and $$S_1S_2^{-1}$$. Zbl 0236.62039
Krishnaiah, P. R.; Chang, T. C.
1970
Tables for the probability integrals of the bivariate $$t$$ distribution. Zbl 0249.65002
Krishnaiah, P. R.; Armitage, J. V.; Breiter, M. C.
1969
Tests for the equality of covariance matrices under the intraclass correlation model. Zbl 0166.15201
Krishnaiah, P. R.; Pathak, P. K.
1968
Simultaneous tests for the equality of covariance matrices against certain alternatives. Zbl 0162.50205
Krishnaiah, P. R.
1968
A note on confidence bounds for certain ratios of characteristic roots of co-variance matrices. Zbl 0177.46404
Krishnaiah, P. R.; Pathak, P. K.
1968
A note on moments of gamma order statistics. Zbl 0147.18806
Krishnaiah, P. R.; Rizvi, M. H.
1967
Tables for the moments of gamma order statistics. Zbl 0164.18808
Breiter, M. C.; Krishnaiah, P. R.
1967
...and 8 more Documents
all top 5

Cited by 560 Authors

 31 Krishnaiah, Paruchuri Rama 28 Bai, Zhi-Dong 13 Fujikoshi, Yasunori 11 Silverstein, Jack W. 9 Gupta, Arjun Kumar 7 Boik, Robert J. 7 Zhao, Lincheng 6 Bhandary, Madhusudan 6 Cabral, Celso Rômulo Barbosa 6 Konishi, Sadanori 6 Lachos Dávila, Víctor Hugo 6 Pan, Guangming 6 Zhou, Wang 5 Jin, Baisuo 5 Kundu, Debasis 5 Oda, Ryoya 5 Péché, Sandrine 5 Yin, Y.-Q. 5 Zheng, Shurong 4 Bose, Arup 4 El Karoui, Noureddine 4 Koreisha, Sergio G. 4 Ledoit, Olivier 4 Miao, Bai-qi 4 Nkiet, Guy Martial 4 Paul, Debashis 4 Perlman, Michael D. 4 Pukkila, Tarmo Mikko 4 Schott, James R. 4 Waikar, Vasant B. 4 Yanagihara, Hirokazu 4 Yao, Jianfeng 3 Balakrishnan, Narayanaswamy 3 Chen, Pinyuen 3 Coelho, Carlos Agra 3 Dauxois, Jacques 3 Davis, Arthur W. 3 Dey, Dipak Kumar 3 Edelman, Alan Stuart 3 Heiny, Johannes 3 Hu, Jiang 3 Isogawa, Yoshiko 3 Jensen, Donald R. 3 Jiang, Tiefeng 3 Joarder, Anwar H. 3 Khan, Shahjahan 3 Kuriki, Satoshi 3 Li, Huiqin 3 Malik, Henrick John 3 Merlevède, Florence 3 Nagao, Hisao 3 Nagarsenker, Brahmanand N. 3 Qin, Yingli 3 Rao, Calyampudi Radhakrishna 3 Rebrova, Elizaveta 3 Romain, Yves 3 Royen, Thomas 3 Schuurmann, Frederick J. 3 Sen, Pranab Kumar 3 Seo, Takashi 3 Siotani, Minoru 3 Spurrier, John D. 3 Subramanyam, Kasala 3 Tikhomirov, Konstantin E. 3 Vershynin, Roman 3 Wolf, Michael 3 Yunus, Rossita Muhamad 3 Zhu, Lixing 2 Agresti, Alan 2 Ahmed, Syed Ejaz 2 Amemiya, Yasuo 2 Andersson, Steen Arne 2 Arslan, Olcay 2 Aue, Alexander 2 Auffinger, Antonio 2 Bhargava, Anil K. 2 Bhaskara Rao, M. 2 Bordenave, Charles 2 Bryc, Włodzimierz 2 Chafaï, Djalil 2 Cheong, Young-Ho 2 Cohen, Arthur 2 Coull, Brent A. 2 Dharmawansa, Prathapasinghe 2 Doğru, Fatma Zehra 2 Dufour, Jean-Marie 2 Farnoosh, Rahman 2 Gagliardini, Patrick 2 Garren, Steven T. 2 Girko, Vyacheslav Leonidovich 2 Guyon, Xavier 2 Harding, Matthew C. 2 Hayakawa, Takesi 2 Hazra, Rajat Subhra 2 Holland, Burt S. 2 Huang, Mong-Na Lo 2 Hušková, Marie 2 Kabe, Dattatraya Govind 2 Kariya, Takeaki 2 Kennedy, William J. jun. ...and 460 more Authors
all top 5

Cited in 97 Serials

 121 Journal of Multivariate Analysis 39 Communications in Statistics. Theory and Methods 26 Annals of the Institute of Statistical Mathematics 24 Journal of Statistical Planning and Inference 19 The Annals of Statistics 17 Statistics & Probability Letters 14 Computational Statistics and Data Analysis 11 Probability Theory and Related Fields 10 Communications in Statistics. Simulation and Computation 9 Journal of Statistical Computation and Simulation 8 The Annals of Probability 8 Journal of Econometrics 7 Journal of Theoretical Probability 7 Bernoulli 6 Journal of Mathematical Physics 6 The Annals of Applied Probability 6 Linear Algebra and its Applications 6 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 4 The Canadian Journal of Statistics 4 American Journal of Mathematical and Management Sciences 4 Statistics 4 Sequential Analysis 4 Test 3 Metrika 3 Advances in Mathematics 3 Biometrical Journal 3 Statistical Science 3 Computational Statistics 3 Pattern Recognition 3 Stochastic Processes and their Applications 3 Electronic Journal of Statistics 3 Random Matrices: Theory and Applications 2 Communications in Mathematical Physics 2 Israel Journal of Mathematics 2 Ukrainian Mathematical Journal 2 Mathematics of Computation 2 Applied Mathematics and Computation 2 Proceedings of the American Mathematical Society 2 Trabajos de Estadistica y de Investigacion Operativa 2 Journal of Time Series Analysis 2 Acta Mathematicae Applicatae Sinica. English Series 2 Journal of Complexity 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Statistical Papers 2 Journal of Nonparametric Statistics 2 Journal of the Korean Statistical Society 2 EURASIP Journal on Advances in Signal Processing 2 Journal of Statistical Theory and Practice 2 Sankhyā. Series A 2 Japanese Journal of Statistics and Data Science 1 Advances in Applied Probability 1 Communications on Pure and Applied Mathematics 1 Discrete Mathematics 1 International Journal of Mathematical Education in Science and Technology 1 International Journal for Numerical and Analytical Methods in Geomechanics 1 Indian Journal of Pure & Applied Mathematics 1 Journal of the Franklin Institute 1 Psychometrika 1 Aplikace Matematiky 1 Automatica 1 Hiroshima Mathematical Journal 1 Journal of Functional Analysis 1 Journal of Mathematical Psychology 1 Journal of Soviet Mathematics 1 Mathematics of Operations Research 1 Statistica Neerlandica 1 Theoretical Population Biology 1 Revue de Statistique Appliquée 1 Acta Applicandae Mathematicae 1 Journal of Symbolic Computation 1 Mathematical and Computer Modelling 1 Stochastic Hydrology and Hydraulics 1 Journal of the Japanese Society of Computational Statistics 1 Science in China. Series A 1 Multidimensional Systems and Signal Processing 1 Random Structures & Algorithms 1 Japan Journal of Industrial and Applied Mathematics 1 Expositiones Mathematicae 1 Journal of Mathematical Sciences (New York) 1 Statistica Sinica 1 Electronic Journal of Probability 1 Discrete and Continuous Dynamical Systems 1 The Journal of Fourier Analysis and Applications 1 Mathematical Problems in Engineering 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 Statistical Inference for Stochastic Processes 1 Econometric Theory 1 Journal of Applied Mathematics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Mathematical Biosciences and Engineering 1 Statistical Methodology 1 Naval Research Logistics Quarterly 1 The Annals of Applied Statistics 1 Analysis & PDE 1 Probability Surveys 1 Science China. Mathematics 1 Afrika Matematika
all top 5

Cited in 32 Fields

 396 Statistics (62-XX) 131 Probability theory and stochastic processes (60-XX) 87 Linear and multilinear algebra; matrix theory (15-XX) 46 Numerical analysis (65-XX) 9 Combinatorics (05-XX) 9 Information and communication theory, circuits (94-XX) 8 Special functions (33-XX) 7 Computer science (68-XX) 6 History and biography (01-XX) 6 Statistical mechanics, structure of matter (82-XX) 6 Operations research, mathematical programming (90-XX) 6 Systems theory; control (93-XX) 5 Functional analysis (46-XX) 5 Biology and other natural sciences (92-XX) 3 Approximations and expansions (41-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Quantum theory (81-XX) 2 Convex and discrete geometry (52-XX) 2 Geophysics (86-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Number theory (11-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Sequences, series, summability (40-XX) 1 Operator theory (47-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX)