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Rao’s statistic for constant and proportional hazard models. (English) Zbl 1153.62002

Summary: We introduce a new family of measures of divergence for the analysis of the degree of departure from a model with a constant hazard function and also for comparing if two models have proportional hazard rates. Our family of measures is based on the family of divergences introduced by J. Burbea and C. R. Rao [On the convexity of higher order Jensen differences based on entropy functions. IEEE Trans. Inf. Theory 28, 961–963 (1982; Zbl 0497.94002)]. Some well-known sets of data are reanalyzed using the new families of test statistics and confidence intervals introduced in this paper.

MSC:

62B10 Statistical aspects of information-theoretic topics
62E20 Asymptotic distribution theory in statistics
62F03 Parametric hypothesis testing

Citations:

Zbl 0497.94002
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References:

[1] Bhattacharya, B., Measures of departure from constant failure rate models and proportional hazards rate models for grouped data, Biometrical Journal, 41, 2, 187-196 (1999) · Zbl 0937.62101
[2] Bhattacharya, B., Csiszar divergence from constant failure rate model for grouped data, Communications in Statistics (Theory and Methods), 30, 6, 1131-1141 (2001) · Zbl 1008.62594
[3] Burbea, J., J-divergences and related topics, Encyclopedia Statistics Science, 44, 290-296 (1983)
[4] Burbea, J.; Rao, C. R., On the convexity of some divergence measures based on entropy functions, IEEE Transactions on Information Theory, 28, 489-495 (1982) · Zbl 0479.94009
[5] Burbea, J.; Rao, C. R., On the convexity of higher order Jensen differences based on entropy functions, IEEE Transactions on Information Theory, 28, 961-963 (1982) · Zbl 0497.94002
[6] Dik, J. J.; Gunst, M. C.M., The distribution of general quadratic forms in normal variables, Statistica Neerlandica, 39, 14-26 (1985) · Zbl 0591.62043
[7] Fraser, D. A.S., Nonparametric Methods in Statistics (1957), John Wiley & Sons: John Wiley & Sons New York · Zbl 0077.12903
[8] Havrda, M. E.; Charvat, F., Quantification method of classification processes: Concept of structural \(\alpha \)-entropy, Kybernetika, 3, 30-35 (1975) · Zbl 0178.22401
[9] Jensen, D. R.; Solomon, H., A Gaussian approximation to the distribution of a definite quadratic form, Journal of the American Statistical Association, 67, 898-902 (1972) · Zbl 0254.62013
[10] Kapur, J. N., Measures of uncertainty, mathematical programming and physics, Journal of the Indian Society Agricultural and Statistics, 24, 47-66 (1972)
[11] Kuonen, D., Saddlepoint approximations for distributions of quadratic forms in normal variables, Biometrika, 86, 929-935 (1999) · Zbl 0942.62021
[12] Mendelhall, W.; Hader, R. J., Estimation of parameters of mixed exponentially distributed failure time distributions from censored life test data, Biometrika, 45, 504-520 (1958) · Zbl 0088.12302
[13] M.L. Menéndez, On Burbea-Rao divergence measures in constant and proportional Hazard models, Technical Report 2007/025, Department of Applied Mathematics. E.T.S.A.M. Technical University of Madrid. 2007; M.L. Menéndez, On Burbea-Rao divergence measures in constant and proportional Hazard models, Technical Report 2007/025, Department of Applied Mathematics. E.T.S.A.M. Technical University of Madrid. 2007
[14] Menéndez, M. L.; Pardo, J. A.; Pardo, L., Rao’s statistic for the analysis of uniform association in cross-classifications, Communications in Statistics (Theory and Methods), 30, 12, 2655-2681 (2001) · Zbl 1009.62552
[15] Modarres, R.; Jernigan, R. W., Testing the equality of correlation matrices, Communications in Statistics (Theory and Methods), 21, 8, 2107-2125 (1992) · Zbl 0777.62059
[16] Pardo, L., Statistical Inference Based on Divergence Measures. Statistics: Textbooks and Monographs (2006), Chapman & Hall/CRC: Chapman & Hall/CRC New York
[17] Pardo, M. C., On Burbea-Rao divergences based goodness-of-fit tests for multinomial models, Journal of Multivariate Analysis, 69, 65-87 (1999) · Zbl 0947.62008
[18] Pardo, M. C.; Vajda, I., About distances of discrete distributions satisfying the data processing theorem of information theory, IEEE Transactions on Information Theory, 43, 4, 1288-1293 (1997) · Zbl 0884.94015
[19] Rao, C. R., Diversity and dissimilarity coefficients: An unified approach, Journal Theoretical Population Biology, 21, 24-43 (1982) · Zbl 0516.92021
[20] Rao, J. N.K.; Scott, A. J., The analysis of categorical data from complex data surveys: Chi-squared tests for goodness-of-fit and independence in two-way table, Journal of the American Statistical Association, 76, 221-230 (1981) · Zbl 0473.62010
[21] Satterthwaite, F. E., An approximate distribution of estimates of variance components, Biometrics, 2, 110-114 (1946)
[22] Vajda, I., Theory of Statistical Inference and Information (1989), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0678.62035
[23] Vajda, I.; Vasek, K., Majorization, concave entropies and comparison of experiments, Problems Control and Information Theory, 14, 105-115 (1985) · Zbl 0601.62006
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