Global statistical information in exponential experiments and selection of exponential models
type: Item
instance of: scholarly article
title: Global statistical information in exponential experiments and selection of exponential models
zbMATH Open document ID: 0937.62006
DOI: 10.1023/A:1022244007831
author: Igor Vajda
author: Edward C. van der Meulen
published in: Applications of Mathematics
publication date: 2000-05-22T00:00:00Z
full work available at URL: https://eudml.org/doc/32995
review text: The paper deals with a classical statistical experiment producing a sequence of iid observations \(X_1,\ldots ,X_n\) with distribution \(P_{\vartheta _0}\) from an exponential family of distributions. The concept of global statistical information \(I_{\vartheta _0}(S)\) is applied in this context. The global information has been introduced in a paper of \textit{I. Vajda} [Global statistical information, likelihood ratio test and maximum likelihood estimators. Kybernetika, submitted 1997]. It evaluates the amount of evidence per observation in favour of the hypothesis that the true parameter \(\vartheta _0\) lies in a given subset \(S\) of the parametric space \(\Theta\). Explicit formulas are given for common exponential families of distributions. One of the main results of the paper shows that the generalized likelihood ratio test procedure of model selection can be replaced by an information procedure that is based just on the global information. This procedure is compared with that one based on the Akaike criterion using simulations in classical regression models.
Mathematics Subject Classification ID: 62B15
Mathematics Subject Classification ID: 62B10
Mathematics Subject Classification ID: 62F05
zbMATH DE Number: 1450139
zbMATH Keywords: global information
zbMATH Keywords: exponential families
zbMATH Keywords: information divergence
zbMATH Keywords: Akaike criterion
reviewed by: Tomáš Cipra
MaRDI profile type: Publication
cites work: Q4769776
cites work: Model selection by multiple test procedures
cites work: Identification of a univariate ARMA model
cites work: Q3995193
cites work: On the Distribution of the Likelihood Ratio
cites work: Q3260839
cites work: Q3747485
cites work: Q3803964
cites work: Maximum likelihood principle and model selection when the true model is unspecified
cites work: Order estimation in ARMA-models by Lagrangian multiplier tests
cites work: Modeling by shortest data description
cites work: Estimating the Order of Hidden Markov Models
cites work: Q3747471
cites work: Estimating the dimension of a model
cites work: Q4728091
cites work: Model selection and prediction: Normal regression
cites work: Order Choice in Nonlinear Autoregressive Models
OpenAlex ID: W206631494
description: scientific article; zbMATH DE number 1450139