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

Tze Fen Li, Dinesh Bhoj

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)245-250
Number of pages6
JournalCanadian Journal of Statistics
Volume14
Issue number3
DOIs
StatePublished - Jan 1 1986

Fingerprint

Minimax Estimator
Bayes Estimator
Multivariate Normal Distribution
Prior distribution
Zero vector
Estimator
Unit matrix
Gamma distribution
Monte Carlo Study
Decision problem
Covariance matrix
Gaussian distribution
Demonstrate
Family
Class
Multivariate normal distribution
Minimax

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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

In: Canadian Journal of Statistics, Vol. 14, No. 3, 01.01.1986, p. 245-250.

Research output: Contribution to journalArticle

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