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 language | English (US) |
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Pages (from-to) | 81-97 |
Number of pages | 17 |
Journal | Annals of the Institute of Statistical Mathematics |
Volume | 47 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1995 |
Keywords
- Empirical Bayes estimation
- convergence rates
- multiple linear regression model
ASJC Scopus subject areas
- Statistics and Probability