On a relation between higher order asymptotic risk sufficiency and higher order asymptotic sufficiency in a local sense
type: Item
instance of: scholarly article
title: On a relation between higher order asymptotic risk sufficiency and higher order asymptotic sufficiency in a local sense
zbMATH Open document ID: 0689.62022
author: Takeru Suzuki
published in: Osaka Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Let (\({\mathcal X},{\mathcal A}_ n,P_{\theta,n}),\theta \in \Theta\), be a family of probability spaces with \(\Theta\) being Euclidean. Let \(\{\) \({\mathcal B}_ n\}\) be a sequence of sub \(\sigma\)-fields of \(\{\) \({\mathcal A}_ n\}\), and \(r_ n^{{\mathcal B}_ n}(c;\theta,\theta ')\) be the Bayes risk of the problem of testing a hypothesis \(``P_{\theta ',n}\) is true'' against an alternative \(``P_{\theta,n}\) is true'' with an experiment (\({\mathcal X},{\mathcal B}_ n,\{P_{\theta ',n},P_{\theta,n}\})\) relative to a prior probability distribution \((c/(1+c)\), \(1/(1+c))\) on \(\{\theta ',\theta \}\). The author gives a sufficient condition for the Bayes risk \(r_ n^{{\mathcal B}_ n}\) for \(\{\) \({\mathcal B}_ n\}\) to be a higher order locally asymptotically sufficient sequence of \(\sigma\)- fields.
Mathematics Subject Classification ID: 62F05
Mathematics Subject Classification ID: 62C10
Mathematics Subject Classification ID: 62F15
zbMATH DE Number: 4129806
zbMATH Keywords: asymptotic risk
zbMATH Keywords: sufficiency
zbMATH Keywords: Bayes risk
zbMATH Keywords: higher order locally asymptotically sufficient
reviewed by: Liqin Zhao
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4129806