Estimation of functionals of an a priori density
type: Item
instance of: scholarly article
title: Estimation of functionals of an a priori density
zbMATH Open document ID: 0659.62048
DOI: 10.1007/BF01097898
author: M. Ya. Penskaya
published in: Journal of Soviet Mathematics
publication date: 1988-01-01T00:00:00Z
review text: We are concerned with the estimation of linear and quadratic functionals of the form \[ (1)\quad \Phi (g)=\int_{\Theta}\phi (\theta)g(\theta)\mu (d\theta),\quad and\quad (2)\quad \Omega (g)=\int_{\Theta}\omega (\theta)g^ 2(\theta)\mu (d\theta) \] in an unknown a priori density. One of the methods for obtaining the desired estimates is to estimate first g(\(\theta)\) and then substitute the result in formulas (1) and (2). However, this method is not always effective since the estimation of g(\(\theta)\) is rather tedious and the estimates are biased. We consider here a different approach which permits at once to estimate the functionals (1) and (2) and, in the case of \(\Phi\) (g), allows us to obtain an unbiased estimate with dispersion of order \(N^{-1}\).
Mathematics Subject Classification ID: 62G05
zbMATH DE Number: 4078519
zbMATH Keywords: exponential distribution with random scale parameter
zbMATH Keywords: estimation of functionals of prior densities
zbMATH Keywords: estimation of linear and quadratic functionals
MaRDI profile type: Publication
cites work: Q4101268
description: scientific article; zbMATH DE number 4078519