Estimation under invariant distributions
type: Item
instance of: scholarly article
title: Estimation under invariant distributions
zbMATH Open document ID: 0669.62014
DOI: 10.1016/0378-3758(89)90064-5
author: Hajime Yamato
author: Yoshihiko Maesono
published in: Journal of Statistical Planning and Inference
publication date: 1989-01-01T00:00:00Z
review text: If a distribution is invariant under a finite group of transformations, an estimator of a parameter associated with the distribution is improved by making it invariant. The resulting invariant estimator is characterized as the projection of the original estimator. If the estimator is the uniformly minimum variance unbiased estimator of its expectation for continuous distributions, then the invariant estimator is the uniformly minimum variance unbiased estimator for invariant and continuous distributions. A typical example is U-statistics and invariant U-statistics.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62A01
zbMATH DE Number: 4096570
zbMATH Keywords: finite group of transformations
zbMATH Keywords: invariant estimator
zbMATH Keywords: projection
zbMATH Keywords: uniformly minimum variance unbiased estimator
zbMATH Keywords: U-statistics
zbMATH Keywords: invariant U- statistics
MaRDI profile type: Publication
full work available at URL: 0378-3758(89)90064-5
OpenAlex ID: W2092213901
cites work: Q4197800
cites work: Q3672893
cites work: Q3311491
cites work: Q3857500
cites work: Invariant U-statistics
cites work: Nonparametric bayes estimates of estimable parameters with a dirichlet invarant process and inveriant u-statistics
description: scientific article; zbMATH DE number 4096570