Sufficiency and invariance
type: Item
instance of: scholarly article
title: Sufficiency and invariance
zbMATH Open document ID: 0575.62006
DOI: 10.1016/0167-7152(85)90044-6
author: Steven F. Arnold
published in: Statistics \& Probability Letters
publication date: 1985-01-01T00:00:00Z
review text: Suppose that a statistical decision problem is invariant under a group of transformations \(g\in G\). T(X) is equivariant if there exists \(g^*\in G^*\) such that \(T(g(X))=g^*(T(X))\). We show that the minimal sufficient statistic is equivariant and that if T(X) is an equivariant sufficient statistic and d(X) is invariant under G, then \(d^*(T)=Ed(X)| T\) is invariant under \(G^*\).
Mathematics Subject Classification ID: 62B05
Mathematics Subject Classification ID: 62A01
Mathematics Subject Classification ID: 62C05
zbMATH DE Number: 3919527
zbMATH Keywords: invariance
zbMATH Keywords: equivariant
zbMATH Keywords: minimal sufficient statistic
MaRDI profile type: Publication
full work available at URL: 0167-7152(85)90044-6
OpenAlex ID: W1972783921
cites work: Q3660706
cites work: Q5532825
cites work: The Relationship Between Sufficiency and Invariance with Applications in Sequential Analysis
cites work: Q3125741
description: scientific article; zbMATH DE number 3919527