Identifying the closest symmetric distribution or density function
type: Item
instance of: scholarly article
title: Identifying the closest symmetric distribution or density function
zbMATH Open document ID: 0638.62025
author: Eugene F. Schuster
published in: The Annals of Statistics
publication date: 1987-01-01T00:00:00Z
review text: This paper addresses the problem of estimating the ``closest'' symmetric distribution or density function to the underlying distribution or density of a data sample, where closeness is measured by any of several (weighted) norms. The main results of the paper say that the ``closest'' symmetric distribution to the empirical distribution \(F_ n\) in various norms is of the form \[ \{F_ n(x)+1-F_ n((2\theta_ n-x)-)\}/2 \] for a suitable estimator \(\theta_ n\) of the ``best location of symmetry''. In the special cases of unweighted sup-norm and integrated square error norm, the explicit forms of the estimators \(\theta_ n\) are given. Analogous results are presented for closest symmetric densities.
Mathematics Subject Classification ID: 62E99
Mathematics Subject Classification ID: 62G99
zbMATH DE Number: 4041043
zbMATH Keywords: weighted sup norm
zbMATH Keywords: weighted \(L_ p\) norm
zbMATH Keywords: Hellinger distance
zbMATH Keywords: symmetrical bootstrap
zbMATH Keywords: minimum distance
zbMATH Keywords: closest distributions
zbMATH Keywords: symmetric distribution
zbMATH Keywords: closeness
zbMATH Keywords: empirical distribution
zbMATH Keywords: best location of symmetry
zbMATH Keywords: unweighted sup-norm
zbMATH Keywords: integrated square error norm
zbMATH Keywords: closest symmetric densities
reviewed by: Eric V. Slud
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350380
OpenAlex ID: W2042532475
DOI: 10.1214/AOS/1176350380
description: scientific article; zbMATH DE number 4041043