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

Laisheng Wei, Shunpu Zhang

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Empirical Bayes (EB) estimation of the parameter vector θ{symbol}=(β′,σ2)′ in a multiple linear regression model Y=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{symbol} 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 are O(n-(λk-1)(k-2)/k(2 k+p+1)), where the natural number k≥3, 1/3<λ<1, and p is the dimension of vector β.

Original languageEnglish (US)
Pages (from-to)81-97
Number of pages17
JournalAnnals of the Institute of Statistical Mathematics
Issue number1
StatePublished - Jan 1 1995



  • Empirical Bayes estimation
  • convergence rates
  • multiple linear regression model

ASJC Scopus subject areas

  • Statistics and Probability

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