On improved estimation in multivariate Dirichlet regressions

Tatiane F. N. Melo, Tiago M. Vargas, Artur J. Lemonte and Germán Moreno–Arenas

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 23, 5765-5777

Abstract: In this paper we consider the multivariate Dirichlet regression model proposed by Melo et al. (2009), which is tailored to situations where the multivariate response consists of multivariate positive observations summing to one and the regression structure involves regressors and unknown parameters. We discuss maximum likelihood estimation for the model parameters and derive modified maximum likelihood estimators that are bias-free to second order. Monte Carlo simulation experiments are conducted in order to investigate the performance of the corrected estimators. The numerical results reveal that the bias correction scheme yields nearly unbiased estimates without increasing the mean squared errors. An empirical application is considered for illustrative purposes.

Date: 2020
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DOI: 10.1080/03610926.2019.1620955

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