Minimax invariant estimator of a continuous distribution function
type: Item
instance of: scholarly article
title: Minimax invariant estimator of a continuous distribution function
zbMATH Open document ID: 0784.62006
DOI: 10.1007/BF00053401
published in: Annals of the Institute of Statistical Mathematics
publication date: 1993-08-25T00:00:00Z
review text: Let \(X_ 1,X_ 2,\dots,X_ n\) be a random sample from an unknown continuous distribution function \(F\). Let \(A=\{a(t): a(t)\) is a nondecreasing function from \((0,1)\) into \([0,1]\}\) be the action space for the estimation of \(F\). The problem under consideration is the invariant estimation of \(F\) under the loss function \[ L(F,a)=\int| F(t)- a(t)|^ k h(F(t))\,dF(t) \] with \(k\geq 1\) and \(h(t)\geq 0\). It has long been conjectured that the best invariant estimator of \(F\) is minimax for all sample sizes \(n\geq 1\). The author proves this conjecture under the preceding wide class of loss functions.
reviewed by: Rasul A. Khan
Mathematics Subject Classification ID: 62C20
Mathematics Subject Classification ID: 62C99
Mathematics Subject Classification ID: 62G05
zbMATH DE Number: 370612
zbMATH Keywords: loss function
zbMATH Keywords: best invariant estimator
author: Qiqing Yu
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00053401
OpenAlex ID: W2027818858
description: scientific article; zbMATH DE number 370612