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Characterization of admissible linear estimators in the growth curve model with respect to inequality constraints. (English) Zbl 1296.62020

Summary: In terms of the theory of inequality and the vectorization transformation of a matrix, we study the admissibility problem of linear estimators in growth curve models with inequality constraints. Under the quadratic loss and the matrix loss, we obtain the necessary and sufficient conditions for a linear estimator of estimable/inestimable linear functions being admissible in the homogeneous and inhomogeneous classes separately.

MSC:

62C15 Admissibility in statistical decision theory
62F10 Point estimation
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[1] Baksalary, J. K.; Markiewiczbq, A.; Rao, C. R., Admissible linear estimation in the general Gauss-Markov model with respect to an arbitrary quadratic risk function, Journal of Statistical Planning and Inference, 44, 341-347 (1995) · Zbl 0811.62064
[2] Cao, M.; Kong, F., Admissibility for linear estimator of parameter on growth curve model with respect to linear constraint, Acta Mathematicae Applicatae Sinica. English Series, 25, 1, 171-176 (2009) · Zbl 1175.62053
[3] Deng, Q. R.; Chen, J. B., Admissibility of nonhomogeneous linear estimators in linear model with respect to an incomplete ellipsoidal restriction under matrix loss function, Chinese Annals of Mathematics, 18A, 33-40 (1997)
[4] Dong, L.; Wu, Q., The sufficient and necessary conditions of admissible linear estimates for random regression coefficients and parameters under the quadratic loss function, Acta Mathematica Scientia, 31, 145-157 (1988) · Zbl 0669.62036
[5] Hoffmann, K., Admissibility of linear estimators with respect to restricted parameter sets, Statistics, 8, 425-438 (1977) · Zbl 0387.62007
[6] LaMotte, L. R., Admissibility in linear estimation, The Annals of Statistics, 10, 1, 245-255 (1982) · Zbl 0485.62070
[7] Lee, J. C., Prediction and estimation of growth curves with special covariance structure, Journal of the American Statistical Association, 83, 402, 432-440 (1988) · Zbl 0648.62074
[8] Lu, C. Y., Admissibility of inhomogeneous linear estimators in linear model with respect to an incomplete ellipsoidal restriction, Communications in Statistics—Theory and Methods, 24, 1737-1742 (1995) · Zbl 0937.62545
[9] Lu, C. Y., The theory of admissibility parameters estimation in linear models, Chinese Journal of Applied Probability and Statistics, 17, 203-212 (2001) · Zbl 1155.62309
[10] Lu, C. Y.; Shi, N. Z., Admissible linear estimators in linear models with respect to inequality constraints, Linear Algebra and its Applications, 354, 187-194 (2002) · Zbl 1009.62006
[11] Polthoff, R. F.; Roy, S. N., A generalized multivariate analysis of variance model useful especially for growth curve problems, Biometrika, 51, 313-326 (1964) · Zbl 0138.14306
[12] Rao, C. R., Estimation of parameters in a linear model, The Annals of Statistics, 4, 1023-1037 (1976) · Zbl 0336.62055
[13] Rao, C. R., Prediction of future observation in growth curve models, Statistical Science, 214, 434-471 (1987) · Zbl 0955.62551
[14] Rosen, D. V., The growth curve model: a review, Communications in Statistics—Theory and Methods, 20, 2791-2822 (1991) · Zbl 0800.62450
[15] Stȩpniak, C., Matrix loss in comparison of linear experiments, Linear Algebra and its Applications, 264, 341-348 (1997) · Zbl 0904.62006
[16] Tian, Y.; Takane, Y., On consistency, natural restrictions and estimability under classical and extended growth curve models, Journal of Statistical Planning and Inference, 139, 2445-2458 (2009) · Zbl 1160.62051
[17] Wong, C. S.; Chang, H., Estimation in a growth curve model with singular covariance, Journal of Statistical Planning and Inference, 97, 323-342 (2001) · Zbl 1015.62056
[18] Wu, J. H., Admissibility of linear estimators in multivariate linear models with respect to inequality constraints, Linear Algebra and its Applications, 428, 2040-2048 (2008) · Zbl 1131.62004
[19] Zhang, S. L.; Gui, W. H., Admissibility of linear estimators in a growth curve model subject to an incomplete ellipsoidal restriction, Acta Mathematica Scientia, 28, 1, 194-200 (2008) · Zbl 1150.62001
[20] Zhang, S. L.; Gui, W. H.; Liu, G., Characterization of admissible linear estimators in the general growth curve model with respect to an incomplete ellipsoidal restriction, Linear Algebra and its Applications, 431, 120-131 (2009) · Zbl 1162.62002
[21] Zhang, S. L.; Liu, G.; Gui, W. H., Admissibility in the general multivariate linear model with respect to restricted parameter set, Journal of Inequalities and Applications, 2009 (2009), 12, Article ID 718927
[22] Zhang, B. X.; Zhu, X. H., Gauss-Markov and weighted least-squares estimation under a growth curve model, Linear Algebra and its Applications, 321, 387-398 (2000) · Zbl 0966.62034
[23] Zhao, J. X., The admissibility of a parameter estimator under vector loss function, Chinese Journal of Applied Probability and Statistics, 18, 134-140 (2002) · Zbl 1155.62311
[24] Zhu, X. H.; Lu, C. Y., Admissibility of linear estimators in linear model, Chinese Annals of Mathematics, 8A, 220-226 (1987) · Zbl 0631.62005
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