Abstract
Empirical Bayes estimation of the parameter vector θ=(β’,σ2)’ in a multiple linear regression modelY=Xβ+ε is considered, where β is the vector of regression coefficient, ε∽N(0,σI with σ2 unknown. In this paper, we construct the EB estimators of θ by using the kernel estimation of multivariate density function and its partial derivatives. Under some moment conditions on prior distribution we obtain their asymptotic optimality.
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References
Chen Xiru, Introduction to Mathematical Statistics, Science Press, 1981.
Robbins, H., An empirical Bayes approach to statistics, Proc. Third Berkeley Symp. Math. Statist. Prob.Vol. 1, Unic. California Press, 1955, 157–163.
Singh, R.S., Empirical Bayes estimation in a multiple linear regression model,Ann. Inst. Statist. Math. 37 (1985), 71–86.
Tao Bo, Asymptotically optimal, empirical Bayes estimators for the parameters of normal distribution family,J. Math. Res. Exposition 6 (1986), 157–162.
Wei Laisheng, Empirical Bayes test of regression coefficient in a multiple linear regression model,Acta Math. Appl. Sinica 6 (1990), 251–262.
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The project is supported by the National Natural Science Foundation of China
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Shunpu, Z., Laisheng, W. The asymptotically optimal empirical bayes estimation in multiple linear regression model. Appl. Math. 9, 245–258 (1994). https://doi.org/10.1007/BF02663774
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DOI: https://doi.org/10.1007/BF02663774