The convergence rates of empirical Bayes estimation in a multiple linear regression model

  • Laisheng Wei
  • Shunpu Zhang
Estimation And Prediction

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,σ2I) 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.

Key words and phrases

Empirical Bayes estimation multiple linear regression model convergence rates 

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Copyright information

© The Institute of Statistical Mathematics 1995

Authors and Affiliations

  • Laisheng Wei
    • 1
  • Shunpu Zhang
    • 2
  1. 1.Department of MathematicsUniversity of Science and Technology of ChinaHefeiChina
  2. 2.Department of MathematicsHangzhou Normal CollegeChina

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