The admissibility of the empirical distribution function
type: Item
instance of: scholarly article
title: The admissibility of the empirical distribution function
zbMATH Open document ID: 0575.62011
author: Michael P. Cohen
author: Lynn Kuo
published in: The Annals of Statistics
publication date: 1985-01-01T00:00:00Z
review text: Consider the problem of estimating an unknown distribution function F from the class of all distribution functions given a random sample of size n from F. It is proved that the empirical distribution function is admissible for the loss functions \[ L(F,\hat F)=\int (\hat F(t)-F(t))^ 2(F(t))^ a(1-F(t))^ bdW(t) \] for any \(a<1\) and \(b<1\) and finite measure W. Related results for simultaneous estimation of distribution functions and for finite population sampling are also given.
Mathematics Subject Classification ID: 62C15
Mathematics Subject Classification ID: 62D05
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 3919532
zbMATH Keywords: weighted quadratic loss
zbMATH Keywords: simple random sampling without replacement
zbMATH Keywords: multinomial distribution
zbMATH Keywords: multivariate hypergeometric distribution
zbMATH Keywords: empirical distribution
zbMATH Keywords: simultaneous estimation
zbMATH Keywords: finite population sampling
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346591
OpenAlex ID: W2041609350
DOI: 10.1214/AOS/1176346591
description: scientific article; zbMATH DE number 3919532