Electronic Journal of Statistics

On estimating a bounded normal mean with applications to predictive density estimation

Éric Marchand, François Perron, and Iraj Yadegari

Full-text: Open access

Abstract

For a normally distributed $X\sim N(\mu,\sigma^{2})$ and for estimating $\mu$ when restricted to an interval $[-m,m]$ under general loss $F(|d-\mu|)$ with strictly increasing and absolutely continuous $F$, we establish the inadmissibility of the restricted maximum likelihood estimator $\delta_{\hbox{mle}}$ for a large class of $F$’s and provide explicit improvements. In particular, we give conditions on $F$ and $m$ for which the Bayes estimator $\delta_{BU}$ with respect to the boundary uniform prior $\pi(-m)=\pi(m)=1/2$ dominates $\delta_{\hbox{mle}}$. Specific examples include $L^{s}$ loss with $s>1$, as well as reflected normal loss. Connections and implications for predictive density estimation are outlined, and numerical evaluations illustrate the results.

Article information

Source
Electron. J. Statist., Volume 11, Number 1 (2017), 2002-2025.

Dates
Received: November 2016
First available in Project Euclid: 16 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1494921828

Digital Object Identifier
doi:10.1214/17-EJS1279

Mathematical Reviews number (MathSciNet)
MR3651022

Zentralblatt MATH identifier
1362.62018

Subjects
Primary: 62C20: Minimax procedures 62C86: Decision theory and fuzziness
Secondary: 62F10: Point estimation 62F15: Bayesian inference 62F30: Inference under constraints

Keywords
Alpha divergence Bayes estimator bounded mean dominance maximum likelihood point estimation predictive density estimation reflected normal loss

Rights
Creative Commons Attribution 4.0 International License.

Citation

Marchand, Éric; Perron, François; Yadegari, Iraj. On estimating a bounded normal mean with applications to predictive density estimation. Electron. J. Statist. 11 (2017), no. 1, 2002--2025. doi:10.1214/17-EJS1279. https://projecteuclid.org/euclid.ejs/1494921828


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