Statistical estimation for truncated exponential families
type: Item
instance of: scholarly article
title: Statistical estimation for truncated exponential families
zbMATH Open document ID: 1383.62002
DOI: 10.1007/978-981-10-5296-5
author: Masafumi Akahira
published in: SpringerBriefs in Statistics
publication date: 2017-11-01T00:00:00Z
review text: The exponential family of distributions with one natural parameter truncated either from one or both sides is considered. Two situations are studied. First, the natural parameter is a parameter of interest while a truncation parameter is considered to be a nuisance parameter. Second, the truncation parameter is a parameter of interest and the natural parameter is a nuisance parameter. The parameter of interest is estimated by a maximum likelihood estimate supposing the nuisance parameter is known and by a bias adjusted maximum likelihood estimate supposing the nuisance parameter is unknown. Moreover, in the case of the natural parameter being the parameter of interest a maximum conditional likelihood estimator is also considered. The second-order asymptotical variances of these estimates obtained from the stochastic expansions are compared. The results are illustrated by several examples, i.e. by a truncated exponential, a truncated normal, an upper-truncated Pareto, a truncated beta and truncated Erlang distributions.
reviewed by: D. Jarušková
Mathematics Subject Classification ID: 62-02
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 62N05
zbMATH DE Number: 6802167
zbMATH Keywords: truncated exponential family
zbMATH Keywords: natural and truncation parameter
zbMATH Keywords: maximum likelihood estimates
zbMATH Keywords: second-order asymptotic variances
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-981-10-5296-5
OpenAlex ID: W2741100852
description: scientific article; zbMATH DE number 6802167