Truncated linear estimation of a bounded multivariate normal mean

Othmane Kortbi, Éric Marchand

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We consider the problem of estimating the mean θ of an N p(θ, I p) distribution with squared error loss ∥δ-θ∥ 2 and under the constraint ∥θ∥≤m, for some constant m>0. Using Stein's identity to obtain unbiased estimates of risk, Karlin's sign change arguments, and conditional risk analysis, we compare the risk performance of truncated linear estimators with that of the maximum likelihood estimator δ mle. We obtain for fixed (m, p) sufficient conditions for dominance. An asymptotic framework is developed, where we demonstrate that the truncated linear minimax estimator dominates δ mle, and where we obtain simple and accurate measures of relative improvement in risk. Numerical evaluations illustrate the effectiveness of the asymptotic framework for approximating the risks for moderate or large values of p.

Original languageEnglish
Pages (from-to)2607-2618
Number of pages12
JournalJournal of Statistical Planning and Inference
Volume142
Issue number9
DOIs
Publication statusPublished - Sep 2012
Externally publishedYes

Keywords

  • Asymptotic analysis
  • Dominance
  • Maximum likelihood
  • Multivariate normal
  • Point estimation
  • Restricted parameters
  • Squared error loss
  • Truncated linear estimators
  • Truncated linear minimax

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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