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.

Estimating the Covariance Matrix of the Maximum Likelihood Estimator Under Linear Cluster-Weighted Models / Soffritti Gabriele. - In: JOURNAL OF CLASSIFICATION. - ISSN 0176-4268. - STAMPA. - 38:3 (October)(2021), pp. 594-625. [10.1007/s00357-021-09390-9]

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

Soffritti Gabriele
2021

Abstract

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.
2021
Estimating the Covariance Matrix of the Maximum Likelihood Estimator Under Linear Cluster-Weighted Models / Soffritti Gabriele. - In: JOURNAL OF CLASSIFICATION. - ISSN 0176-4268. - STAMPA. - 38:3 (October)(2021), pp. 594-625. [10.1007/s00357-021-09390-9]
Soffritti Gabriele
File in questo prodotto:
File Dimensione Formato  
s00357-021-09390-9.pdf

accesso aperto

Descrizione: pdf editoriale
Tipo: Versione (PDF) editoriale
Licenza: Licenza per Accesso Aperto. Creative Commons Attribuzione (CCBY)
Dimensione 1.06 MB
Formato Adobe PDF
1.06 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/855051
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact