Estimating the Covariance Matrix of the Maximum Likelihood Estimator Under Linear Cluster-Weighted Models

Autor:	Gabriele Soffritti
Přispěvatelé:	Soffritti Gabriele
Rok vydání:	2021
Předmět:	Hessian matrix Maximum likelihood Multivariate normal distribution Library and Information Sciences 01 natural sciences 010104 statistics & probability Matrix (mathematics) symbols.namesake Mathematics (miscellaneous) 0504 sociology Cluster (physics) Statistics::Methodology Applied mathematics Linear regression 0101 mathematics Score vector Mathematics Covariance matrix 05 social sciences 050401 social sciences methods Estimator Gaussian mixture model Model-based cluster analysi Pattern recognition (psychology) symbols Psychology (miscellaneous) Statistics Probability and Uncertainty Sandwich estimator
Zdroj:	Journal of Classification. 38:594-625
ISSN:	1432-1343 0176-4268
DOI:	10.1007/s00357-021-09390-9
Popis:	In recent years, the research into cluster-weighted models has been intense. However, estimating the covariance matrix of the maximum likelihood estimator under a cluster-weighted model is still an open issue. Here, an approach is developed in which information-based estimators of such a covariance matrix are obtained from the incomplete data log-likelihood of the multivariate Gaussian linear cluster-weighted model. To this end, analytical expressions for the score vector and Hessian matrix are provided. Three estimators of the asymptotic covariance matrix of the maximum likelihood estimator, based on the score vector and Hessian matrix, are introduced. The performances of these estimators are numerically evaluated using simulated datasets in comparison with a bootstrap-based estimator; their usefulness is illustrated through a study aiming at evaluating the link between tourism flows and attendance at museums and monuments in two Italian regions.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2ffa371d4c365f15260e56b5c14b4c7d https://doi.org/10.1007/s00357-021-09390-9 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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