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

Gabriele Soffritti ()
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Gabriele Soffritti: Alma Mater Studiorum - University of Bologna

Journal of Classification, 2021, vol. 38, issue 3, No 10, 594-625

Abstract: 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.

Keywords: Gaussian mixture model; Hessian matrix; Linear regression; Model-based cluster analysis; Sandwich estimator; Score vector (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00357-021-09390-9

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