Abstract
Empirical Bayes (EB) 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,σ2 I) and σ2 is unknown. In this paper, we have constructed the EB estimators of ϑ by using the kernel estimation of multivariate density function and its partial derivatives. Under suitable conditions it is shown that the convergence rates of the EB estimators areO(n -(λk-1)(k-2)/k(2k+p+1)), where the natural numberk≥3, 1/3<λ<1, andp is the dimension of vector β.
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The project is supported by the National Natural Science Foundation of China.
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Wei, L., Zhang, S. The convergence rates of empirical Bayes estimation in a multiple linear regression model. Ann Inst Stat Math 47, 81–97 (1995). https://doi.org/10.1007/BF00773413
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DOI: https://doi.org/10.1007/BF00773413