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

Laisheng Wei, Shunpu Zhang

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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
Volume47
Issue number1
DOIs
StatePublished - Jan 1 1995

Fingerprint

Empirical Bayes Estimation
Multiple Linear Regression
Linear Regression Model
Empirical Bayes Estimator
Rate of Convergence
Kernel Estimation
Multivariate Functions
Partial derivative
Regression Coefficient
Natural number
Density Function
Unknown

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

The convergence rates of empirical Bayes estimation in a multiple linear regression model. / Wei, Laisheng; Zhang, Shunpu.

In: Annals of the Institute of Statistical Mathematics, Vol. 47, No. 1, 01.01.1995, p. 81-97.

Research output: Contribution to journalArticle

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