Bessel regression model: Robustness to analyze bounded data release_loec2jqxfvacnlt3pwa2b4i43a

by Wagner Barreto-Souza, Vinícius D. Mayrink, Alexandre B. Simas

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2020  

Abstract

Beta regression has been extensively used by statisticians and practitioners to model bounded continuous data and there is no strong and similar competitor having its main features. A class of normalized inverse-Gaussian (N-IG) process was introduced in the literature, being explored in the Bayesian context as a powerful alternative to the Dirichlet process. Until this moment, no attention has been paid for the univariate N-IG distribution in the classical inference. In this paper, we propose the bessel regression based on the univariate N-IG distribution, which is a robust alternative to the beta model. This robustness is illustrated through simulated and real data applications. The estimation of the parameters is done through an Expectation-Maximization algorithm and the paper discusses how to perform inference. A useful and practical discrimination procedure is proposed for model selection between bessel and beta regressions. Monte Carlo simulation results are presented to verify the finite-sample behavior of the EM-based estimators and the discrimination procedure. Further, the performances of the regressions are evaluated under misspecification, which is a critical point showing the robustness of the proposed model. Finally, three empirical illustrations are explored to confront results from bessel and beta regressions.
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Date   2020-03-11
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arXiv  2003.05157v1
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