Bessel regression model: Robustness to analyze bounded data
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by
Wagner Barreto-Souza, Vinícius D. Mayrink, Alexandre B. Simas
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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