Methodology for the invariant estimation of a continuous distribution function
type: Item
instance of: scholarly article
title: Methodology for the invariant estimation of a continuous distribution function
zbMATH Open document ID: 0698.62037
DOI: 10.1007/BF00050665
published in: Annals of the Institute of Statistical Mathematics
publication date: 1989-01-01T00:00:00Z
review text: Invariant estimation of a continuous distribution function with the weighted quadratic loss function and a sample of a fixed size is considered. Let N be the class of invariant estimators. Imposing some additional conditions on estimators, a sequence of more general invariance problems with classes \(U_ m\), \(m=1,2,..\). of invariant estimators is defined. Approximation of estimators from N by estimators from \(U_ m\) is established. Results like ``d is admissible in N iff it is admissible in \(U_ 1\)'' are presented. The problem of minimaxity of estimators is discussed.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62C15
Mathematics Subject Classification ID: 62C20
zbMATH DE Number: 4145141
zbMATH Keywords: nonrandomized estimator
zbMATH Keywords: Lebesgue measure
zbMATH Keywords: finite sample problem
zbMATH Keywords: best invariant estimator
zbMATH Keywords: distribution estimation
zbMATH Keywords: weighted quadratic loss
zbMATH Keywords: class of invariant estimators
zbMATH Keywords: Approximation of estimators
zbMATH Keywords: minimaxity of estimators
author: Qiqing Yu
reviewed by: Ryszard Zieliński
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4145141