A characterization of translation-invariant experiments admitting adaptive estimates
type: Item
instance of: scholarly article
title: A characterization of translation-invariant experiments admitting adaptive estimates
zbMATH Open document ID: 0651.62026
DOI: 10.1016/0047-259X(88)90038-3
author: Georg Ch. Pflug
author: Wilfried Grossmann
published in: Journal of Multivariate Analysis
publication date: 1988-01-01T00:00:00Z
review text: The paper under review completely solves the problem of adaptivity for translation invariant experiments. Recall that an estimator for a parameter t is called adaptive if it ignores a nuisance parameter u of the model without loss in efficiency compared with those procedures where u is known. It is pointed out that by definition adaptivity depends on the underlying loss function which determines the minimax risk. In contrast to the common believe, ``independence of t and u'', i.e. \(P_{t,u}=P_ t\otimes P_ u\), is not responsable for adaptivity. It is shown that the existence of independent posterior distributions is equivalent to the adaptivity property. Three types of limit experiments are discussed: local asymptotic (mixed) normal experiments, and experiments arising from densities with jumps.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62F35
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 62B15
zbMATH DE Number: 4062359
zbMATH Keywords: adaptive estimates
zbMATH Keywords: minimax bounds
zbMATH Keywords: Pitman estimates
zbMATH Keywords: semi-parametric models
zbMATH Keywords: translation invariant experiments
zbMATH Keywords: minimax risk
zbMATH Keywords: existence of independent posterior distributions
zbMATH Keywords: adaptivity property
zbMATH Keywords: limit experiments
zbMATH Keywords: local asymptotic (mixed) normal experiments
reviewed by: Arnold Janssen
Wikidata QID: Q59255217
MaRDI profile type: Publication
cites work: Q3957821
cites work: Information and asymptotic efficiency in parametric-nonparametric models
cites work: On adaptive estimation
cites work: On estimation and adaptive estimation for locally asymptotically normal families
cites work: Q5179663
cites work: Q4171432
cites work: Q3956225
cites work: Q3239659
cites work: Local asymptotic minimax properties of Pitman estimates
cites work: Mathematical theory of statistics. Statistical experiments and asymptotic decision theory
description: scientific article; zbMATH DE number 4062359