The convergence rates of empirical Bayes estimation in a multiple linear regression model |
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Authors: | Laisheng Wei Shunpu Zhang |
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Institution: | (1) Department of Mathematics, University of Science and Technology of China, 230026 Hefei, Anhui, China;(2) Department of Mathematics, Hangzhou Normal College, 310036, Zhejiang, China |
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Abstract: | Empirical Bayes (EB) estimation of the parameter vector =(,2) in a multiple linear regression modelY=X+ is considered, where is the vector of regression coefficient, N(0,2
I) and 2 is unknown. In this paper, we have constructed the EB estimators of 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
-(k-1)(k-2)/k(2k+p+1)), where the natural numberk3, 1/3<<1, andp is the dimension of vector .The project is supported by the National Natural Science Foundation of China. |
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Keywords: | Empirical Bayes estimation multiple linear regression model convergence rates |
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