Behaviour of third order terms in quadratic approximations of LR- statistics in multivariate generalized linear models
type: Item
instance of: scholarly article
title: Behaviour of third order terms in quadratic approximations of LR- statistics in multivariate generalized linear models
zbMATH Open document ID: 0587.62100
author: Christian Kredler
published in: The Annals of Statistics
publication date: 1986-01-01T00:00:00Z
review text: The size of error is investigated when the log-likelihood of multivariate generalized linear models is approximated by a quadratic function. The nonquadratic tail is characterized by analyzing the cubic part of the log-likelihood. In a local analysis simple bounds for that part can be expressed in terms of expectations of the related random variables for arbitrary sample size N. Additionally global error bounds are given for the univariate case.
Mathematics Subject Classification ID: 62H10
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62F03
Mathematics Subject Classification ID: 62J02
zbMATH DE Number: 3942785
zbMATH Keywords: third derivative structure of an exponential family
zbMATH Keywords: third moments
zbMATH Keywords: quadratic approximation error
zbMATH Keywords: variable selection
zbMATH Keywords: size of error
zbMATH Keywords: log- likelihood of multivariate generalized linear models
zbMATH Keywords: global error bounds
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176349859
OpenAlex ID: W1965903691
DOI: 10.1214/AOS/1176349859
description: scientific article; zbMATH DE number 3942785