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\(\Phi\) admissibility of stochastic regression coefficients in a general multivariate random effects model under a generalized balanced loss function. (English) Zbl 1295.62008

Summary: The definitions of \(\Phi\) optimality and \(\Phi\) admissibility of stochastic regression coefficients are given in a general multivariate random effects model under the generalized balanced loss function. \(\Phi\) admissibility of linear estimators of stochastic regression coefficients is investigated. Sufficient and necessary conditions for linear estimators to be \(\Phi\) admissible in classes of homogeneous and nonhomogeneous linear estimators are obtained, respectively.

MSC:

62C15 Admissibility in statistical decision theory
62J12 Generalized linear models (logistic models)
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References:

[1] Arashi, M. (2009). Problem of estimation with balanced loss function in elliptical models., .
[2] Cao, M. (2009a). \(\Phi\) admissibility for linear estimators on regression coefficients in a general multivariate linear model under balanced loss function., J. Statist. Plann. Inference 139 , 3354-3360. · Zbl 1168.62006
[3] Cao, M. (2011). Admissibility of linear estimators for stochastic regression coefficient in a general Gauss-Markoff model under balanced loss function., under review.
[4] Cao, M. and Kong, F. (2009b). Admissibility for linear estimators to regression coefficients in a multivariate linear model., Acta Math. Appl. Sin. 32 , 951-957. · Zbl 1210.62056
[5] Chung, Y. and Kim, C. (1997). Simultaneous estimation of the multivariate normal mean under balanced loss function., Commun. Statist. Theory Methods 26 , 1599-1611. · Zbl 0954.62502
[6] Dey, D. K., Ghosh, M. and Strawderman, W. (1999). On estimation with balanced loss functions., Statist. Probab. Lett. 45 , 97-101. · Zbl 0951.62019
[7] Dong, L. and Wu, Q. (1988). Necessary and sufficient conditions for linear estimators of stochastic regression coefficients and parameters to be admissible under quadratic loss., Acta Mathematics sinica 31 , 145-157. · Zbl 0669.62036
[8] Gruber, M. H. J. (1999)., The efficiency of shrinkage estimators for Zellner’s loss function . In: ASA Meeting (Contributed Paper), Maryland, Baltimore, August.
[9] Gruber, M. H. J. (2004). The efficiency of shrinkage estimators with respect to Zellner’s balanced loss function., Commun. Statist. Theory Methods 33 , 235-249. · Zbl 1102.62073
[10] Hu, G. and Peng, P. (2010). Admissibility for linear estimators of regression coefficient in a general Gauss-Markoff model under balanced loss function., J. Statist. Plann. Inference 140 , 3365-3375. · Zbl 1207.62122
[11] Jafari Jozani, M., Marchand, E. and Parsian, A. (2006). On estimation with weighted banaced-type Loss function., Statist. Probab. Lett. 76 , 773-780. · Zbl 1090.62007
[12] Jafari Jozani, M., Marchand, E. and Parsian, A. (2012). Bayesian and Robust Bayesian analysis under a general class of balanced loss functions., Statist. Papers 53 , 51-60. · Zbl 1241.62004
[13] Kiefer, J. (1974). General equivalence theory for optimum designs., Ann. Statist. 2 , 849-879. · Zbl 0291.62093
[14] Markiewicz, A. (1997). Properties of information matrices for linear models and universal optimality of experimental designs., J. Statist. Plann. Inference 59 , 127-137. · Zbl 0898.62094
[15] Markiewicz, A. (2001). On dependence structures preserving optimality., Statist. Probab. Lett. 53 , 415-419. · Zbl 0983.62041
[16] Markiewicz, A. (2007). Optimal designs in multivariate linear models., Statist. Probab. Lett. 77 , 426-430. · Zbl 1108.62074
[17] Ohtani, K. (1998). The exact risk of a weighted average estimator of the OLS and Stein-rule estimators in regression under balanced loss., Statist. Decisions 16 , 35-45. · Zbl 0888.62069
[18] Ohtani, K. (1999). Inadmissibility of the Stein-rule estimator under the balanced loss function., J. Econometrics 88 , 193-201. · Zbl 0933.62008
[19] Qin, H. (1994). Universal admissibility of linear estimates of regression coefficients in growth curve model., Chin. J. Appl. Prob. Stat. 10 , 265-271. · Zbl 0952.62545
[20] Rodrigues, J and Zellner, A. (1994). Weighted balanced loss function and estimation of the mean time to failure., Commun. Statist. Theory Methods 23 , 3609-3616. · Zbl 0825.62250
[21] Rao, C. R. (1965)., Linear statistical Inference and Its Applications . second edtion, Wiley, NewYork. · Zbl 0137.36203
[22] Toutenburg, H. and Shalabh (2005). Estimation of regression coefficients subject to exact linear restrictions when some observations are missing and quadratic error balanced loss function is used., TEST 14 , 385-396. · Zbl 1087.62068
[23] Xie, M. (1990). Admissibility for linear estimates on multivariate regression coefficients., Chinese Sci. Bull. 35 , 881-883. · Zbl 0702.62008
[24] Xie, M. (1994). Admissibility for linear estimates on regression coefficients in a general multivariate linear model., Acta Math. Sci. (English Ed.) 14 , 329-337. · Zbl 0812.62005
[25] Xie, M. and Zhang, Y. (1993). General optimality and general admissible of linear estimates on the mean matrix., Chinese Sci. Bull. 35 , 1071-1074. · Zbl 0785.62059
[26] Xie, M. (1995). The General admissibility theory of matrix parameter estimation., Chinese J. Appl. Probab. Statist. 11 , 431-438. · Zbl 0953.62503
[27] Xu, L. and Wang, S. (2006). General admissibility of linear predictor in the multivariate random effects model., Acta Math. Appl. Sin. 29 , 116-123.
[28] Xu, X. and Wu, Q. (2000). Linear admissible estimators of regression coefficient under balanced loss., Acta Math. Sci. Ser. A Chin. Ed. 20 , 468-473. · Zbl 0961.62006
[29] Zellner, A. (1994)., Bayesian and non-Bayesian estimation using balanced loss function . Gupta S. S., Berger J. O., eds. Statistical decision theory and related topics V. Spring-Verlag, New York, 377-390. · Zbl 0787.62035
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