An introduction to Bartlett correction and bias reduction
type: Item
instance of: scholarly article
title: An introduction to Bartlett correction and bias reduction
zbMATH Open document ID: 1306.62025
DOI: 10.1007/978-3-642-55255-7
author: Francisco Cribari-Neto
author: Gauss M. Cordeiro
published in: SpringerBriefs in Statistics
publication date: 2014-06-18T00:00:00Z
review text: This monograph deals with two important topics of research among statisticians. The first one is the Bartlett and Bartlett-type corrections that can be applied to test statistics in order to bring the empirical sizes of asymptotic tests close to the corresponding nominal sizes, while the second one is the strategies that can be employed to reduce the bias of the maximum likelihood estimator. The underlying idea behind both groups of corrections is to obtain higher accuracy in small samples. Even though the focus of the authors is to present, in a coherent way, analytical corrections to test statistics and estimators, they also discuss and provide numerical alternatives, which are mainly based on bootstrap resampling, that can be used for the same purpose. In this statistical framework, the monograph consists of four chapters, an appendix, where supplementary material is given, and a glossary. In the sequel, the subject of each one of the four chapters is briefly presented. Chapter 1 (Likelihood-based inference and finite-sample corrections: a brief overview) briefly introduces the likelihood function, maximum likelihood estimators and some of their properties as well as the most commonly asymptotic testing criteria, namely the likelihood ratio (LR), the score test and the Wald test. Moreover, some remarks related to concepts that will be used throughout the book are given. Chapter 2 (Bartlett corrections and bootstrap testing inference) initially provides a unified review of the literature on Bartlett correction to the likelihood ratio test statistic. Afterwards, a discussion on how to obtain the corrections in regression models, such as generalized linear models (GLM) and Birnbaum-Saunders nonlinear regression models is given. Finally, it is described how the bootstrap resampling scheme can be used as an alternative to analytical finite sample corrections for improving on LR testing inference. Chapter 3 (Bartlett-type corrections) provides a unified review of the l…
reviewed by: A. Batsidis
Mathematics Subject Classification ID: 62-02
Mathematics Subject Classification ID: 62-01
Mathematics Subject Classification ID: 62F03
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62F40
zbMATH DE Number: 6305058
zbMATH Keywords: Bartlett corrections
zbMATH Keywords: Bartlett-type corrections
zbMATH Keywords: likelihood ratio
zbMATH Keywords: score test
zbMATH Keywords: hypothesis testing
zbMATH Keywords: maximum likelihood
zbMATH Keywords: bias reduction
zbMATH Keywords: bootstap
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-642-55255-7
OpenAlex ID: W599938562
description: scientific article; zbMATH DE number 6305058