Locally minimax efficiency of nonparametric estimates of square- integrable densities
type: Item
instance of: scholarly article
title: Locally minimax efficiency of nonparametric estimates of square- integrable densities
zbMATH Open document ID: 0806.62026
DOI: 10.1007/BF00970426
author: V. Pereyra
published in: Lithuanian Mathematical Journal
publication date: 1994-07-21T00:00:00Z
review text: The paper gives a necessary and sufficient condition for the existence of the estimate \(f^*\) of the probability density \(f\), such that for any function \(g\in W^ 0\) \[ \sup_{f\in W_ g} E_ f\| f^*-f\|^ 2_ 2 \sim\inf_{\widehat {f}} \sup_{f\in W_ g} E_ f\| \widehat{f}- f\|^ 2_ 2. \] Here \(W^ 0\) is the interior of \(W\subseteq L_ 2\), a subset of all square-integrable probability densities having compact support. Additionally \(f^*\) is given as a minimizer of the first component of a random functional \(G(p,g,h)\) on \(L_ 2\times W\times H\), where \(H\) is the set of all selfadjoined operators from \(L_ 2\) in \(L_ 2\) and \(g\) and \(h\) depend suitably on \(p\).
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 47N30
zbMATH DE Number: 578677
zbMATH Keywords: necessary and sufficient condition
zbMATH Keywords: existence
zbMATH Keywords: square-integrable probability densities
zbMATH Keywords: compact support
zbMATH Keywords: random functional
zbMATH Keywords: selfadjoined operators
reviewed by: Rainer Schlittgen
MaRDI profile type: Publication
cites work: Q4099504
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full work available at URL: https://doi.org/10.1007/bf00970426
OpenAlex ID: W2088606452
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description: scientific article; zbMATH DE number 578677