## Electronic Journal of Statistics

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

#### 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
First available in Project Euclid: 16 May 2017

https://projecteuclid.org/euclid.ejs/1494921828

Digital Object Identifier
doi:10.1214/17-EJS1279

Mathematical Reviews number (MathSciNet)
MR3651022

Zentralblatt MATH identifier
1362.62018

#### 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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