### Abstract

Let X has a p‐dimensional normal distribution with mean vector θ and identity covariance matrix I. In a compound decision problem consisting of squared‐error estimation of θ, Strawderman (1971) placed a Beta (α, 1) prior distribution on a normal class of priors to produce a family of Bayes minimax estimators. We propose an incomplete Gamma(α, β) prior distribution on the same normal class of priors to produce a larger family of Bayes minimax estimators. We present the results of a Monte Carlo study to demonstrate the reduced risk of our estimators in comparison with the Strawderman estimators when θ is away from the zero vector.

Original language | English (US) |
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Pages (from-to) | 245-250 |

Number of pages | 6 |

Journal | Canadian Journal of Statistics |

Volume | 14 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1986 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

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*Canadian Journal of Statistics*, vol. 14, no. 3, pp. 245-250. https://doi.org/10.2307/3314801

**A family of admissible minimax estimators of the mean of a multivariate, normal distribution.** / Li, Tze Fen; Bhoj, Dinesh.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A family of admissible minimax estimators of the mean of a multivariate, normal distribution

AU - Li, Tze Fen

AU - Bhoj, Dinesh

PY - 1986/1/1

Y1 - 1986/1/1

N2 - Let X has a p‐dimensional normal distribution with mean vector θ and identity covariance matrix I. In a compound decision problem consisting of squared‐error estimation of θ, Strawderman (1971) placed a Beta (α, 1) prior distribution on a normal class of priors to produce a family of Bayes minimax estimators. We propose an incomplete Gamma(α, β) prior distribution on the same normal class of priors to produce a larger family of Bayes minimax estimators. We present the results of a Monte Carlo study to demonstrate the reduced risk of our estimators in comparison with the Strawderman estimators when θ is away from the zero vector.

AB - Let X has a p‐dimensional normal distribution with mean vector θ and identity covariance matrix I. In a compound decision problem consisting of squared‐error estimation of θ, Strawderman (1971) placed a Beta (α, 1) prior distribution on a normal class of priors to produce a family of Bayes minimax estimators. We propose an incomplete Gamma(α, β) prior distribution on the same normal class of priors to produce a larger family of Bayes minimax estimators. We present the results of a Monte Carlo study to demonstrate the reduced risk of our estimators in comparison with the Strawderman estimators when θ is away from the zero vector.

UR - http://www.scopus.com/inward/record.url?scp=84988073803&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84988073803&partnerID=8YFLogxK

U2 - 10.2307/3314801

DO - 10.2307/3314801

M3 - Article

AN - SCOPUS:84988073803

VL - 14

SP - 245

EP - 250

JO - Canadian Journal of Statistics

JF - Canadian Journal of Statistics

SN - 0319-5724

IS - 3

ER -