Minimaxity of the empirical distribution function in invariant estimation
type: Item
instance of: scholarly article
title: Minimaxity of the empirical distribution function in invariant estimation
zbMATH Open document ID: 0739.62011
author: Mo-Suk Chow
author: Qiqing Yu
published in: The Annals of Statistics
publication date: 1992-06-25T00:00:00Z
review text: Consider the problem of invariant (under monotone transformations) estimation of continuous distribution functions with Cramér-von Mises loss function weighted by \(h(t)=t^{-1}(1-t)^{-1},\;t\in(0,1)\). The minimaxity of the empirical distribution function which, as is well- known, is the best invariant estimator in this problem, is proved for sample sizes \(n>2\). A detailed proof is given for the case \(n=3\) and under some additional conditions on the class of estimators. The proof for the general case is only outlined.
reviewed by: L.B.Merkulovich
Mathematics Subject Classification ID: 62C20
Mathematics Subject Classification ID: 62G07
zbMATH DE Number: 11543
zbMATH Keywords: finite sample size invariant decision problem
zbMATH Keywords: order statistics
zbMATH Keywords: minimaxity within a class
zbMATH Keywords: Egoroff's theorem
zbMATH Keywords: Baire category theorem
zbMATH Keywords: product measure
zbMATH Keywords: monotone transformations
zbMATH Keywords: Cramér-von Mises loss
zbMATH Keywords: minimaxity of the empirical distribution
zbMATH Keywords: best invariant estimator
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176348129
OpenAlex ID: W2092829808
DOI: 10.1214/AOS/1176348129
description: scientific article; zbMATH DE number 11543