Loss functions for loss estimation
type: Item
instance of: scholarly article
title: Loss functions for loss estimation
zbMATH Open document ID: 0672.62011
published in: The Annals of Statistics
publication date: 1988-01-01T00:00:00Z
review text: Let X be a random variable with distribution \(P_{\theta}\), where \(\theta\in \Theta\), and d(X) a decision for \(\theta\) with loss W(\(\theta\),d(X)). A class of loss functions combining the decision error W(\(\theta\),d(X)) and the error in estimating W(\(\theta\),d(X)) by h(X) is introduced. Under these loss functions the Bayes procedure \((d_ B(X),h_ B(X))\) has the following form: \(d_ B(X)\) is just the Bayes decision corresponding to the loss W(\(\theta\),d(X)) and \(h_ B(X)=E(W(\theta,d_ B(X))| X)\). Under some regularity assumptions, a necessary and sufficient condition for (d(X),h(X)) to be admissible is given.
Mathematics Subject Classification ID: 62C15
Mathematics Subject Classification ID: 62C10
Mathematics Subject Classification ID: 62A01
zbMATH DE Number: 4100373
zbMATH Keywords: proper scoring functions
zbMATH Keywords: expected posterior loss
zbMATH Keywords: posterior risk
zbMATH Keywords: concavity
zbMATH Keywords: loss functions
author: Andrew L. Rukhin
reviewed by: Qiguang Wu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350960
OpenAlex ID: W1985639935
DOI: 10.1214/AOS/1176350960
description: scientific article; zbMATH DE number 4100373