Open Access
Translator Disclaimer
September, 1985 Estimation of a Symmetric Distribution
Shaw-Hwa Lo
Ann. Statist. 13(3): 1097-1113 (September, 1985). DOI: 10.1214/aos/1176349658

Abstract

Suppose that $F_0$ is a population which is symmetric about zero, so that $F(\cdot) = F_0(\cdot - \theta)$ is symmetric about $\theta$. We consider the problem of estimating $F_0$ (shape parameter), both $\theta$ and $F_0$, and $F$ based on a random sample from $F$. First, some asymptotically minimax bounds are obtained. Then, some estimates are constructed which are asymptotically minimax-efficient (the risks of which achieve the minimax bounds uniformly). Furthermore, it is pointed out that one can estimate $F_0$, the shape of $F$, as well without knowing the location parameter $\theta$ as with knowing it. After a slight modification, Stone's (1975) estimator is proved to be asymptotically minimax-efficient in the Hellinger neighborhood.

Citation

Download Citation

Shaw-Hwa Lo. "Estimation of a Symmetric Distribution." Ann. Statist. 13 (3) 1097 - 1113, September, 1985. https://doi.org/10.1214/aos/1176349658

Information

Published: September, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0594.62015
MathSciNet: MR803760
Digital Object Identifier: 10.1214/aos/1176349658

Subjects:
Primary: 62E20
Secondary: 62G20, 62G30

Rights: Copyright © 1985 Institute of Mathematical Statistics

JOURNAL ARTICLE
17 PAGES


SHARE
Vol.13 • No. 3 • September, 1985
Back to Top