The lower bound for the variance of unbiased estimators for one- directional family of distributions
type: Item
instance of: scholarly article
title: The lower bound for the variance of unbiased estimators for one- directional family of distributions
zbMATH Open document ID: 0656.62034
DOI: 10.1007/BF02491492
author: Masafumi Akahira
author: Kei Takeuchi
published in: Annals of the Institute of Statistical Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The concept of one-directionality of a distribution family is introduced, including both cases of location and scale parameters as well as the selection parameters. Some theorems concerning sharp lower bounds for the variance of unbiased estimators and the existence of zero variance unbiased estimators for nonregular distributions are given.
Mathematics Subject Classification ID: 62F10
zbMATH DE Number: 4072133
zbMATH Keywords: Cramér-Rao bound
zbMATH Keywords: Bhattacharyya bound
zbMATH Keywords: one-directionality
zbMATH Keywords: location
zbMATH Keywords: scale
zbMATH Keywords: selection parameters
zbMATH Keywords: sharp lower bounds for the variance of unbiased estimators
zbMATH Keywords: existence of zero variance unbiased estimators
zbMATH Keywords: nonregular distributions
reviewed by: Emiliana Ursianu
MaRDI profile type: Publication
cites work: Bhattacharyya bound of variances of unbiased estimators in nonregular cases
cites work: Minimum Variance Estimation Without Regularity Assumptions
cites work: Bhattacharyya Bounds without Regularity Assumptions
cites work: On Minimum Variance Estimators
cites work: Note on the Cramer-Rao inequality in the nonregular case: The family of uniform distributions
cites work: Q5574466
cites work: A note on minimum variance
cites work: Q3852969
description: scientific article; zbMATH DE number 4072133