### Abstract

Empirical Bayes (EB) estimation of the parameter vector θ{symbol}=(β′,σ^{2})′ in a multiple linear regression model Y=Xβ+ε is considered, where β is the vector of regression coefficient, ε ∼N(0,σ^{2}I) and σ^{2} 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 1 1995 |

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### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

*Annals of the Institute of Statistical Mathematics*,

*47*(1), 81-97. https://doi.org/10.1007/BF00773413

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

Research output: Contribution to journal › Article

*Annals of the Institute of Statistical Mathematics*, vol. 47, no. 1, pp. 81-97. https://doi.org/10.1007/BF00773413

}

TY - JOUR

T1 - The convergence rates of empirical Bayes estimation in a multiple linear regression model

AU - Wei, Laisheng

AU - Zhang, Shunpu

PY - 1995/1/1

Y1 - 1995/1/1

N2 - 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.

AB - 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.

KW - Empirical Bayes estimation

KW - convergence rates

KW - multiple linear regression model

UR - http://www.scopus.com/inward/record.url?scp=0542364616&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0542364616&partnerID=8YFLogxK

U2 - 10.1007/BF00773413

DO - 10.1007/BF00773413

M3 - Article

VL - 47

SP - 81

EP - 97

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

IS - 1

ER -