Joint regression modeling of location and scale parameters of the skew t distribution with application in soil chemistry data. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Prataviera, F.; Batista, A. M.; Libardi, P. L.; Cordeiro, G. M.; Ortega, E. M. M.
• Is Part Of: Journal of applied statistics. Volume 49:Issue 1(2022)
• Page Start: 195
• Page End: 213
• Publication Date: 2022-01-02
• Subjects: Maximum likelihood -- quantile residuals -- regression model -- skew normal -- skew t distribution; Statistics -- Periodicals; 519.5
• DOI: 10.1080/02664763.2020.1801608
• Languages: English
• ISSNs: 0266-4763

Abstract

ABSTRACT: In regression model applications, the errors may frequently present a symmetric shape. In such cases, the normal and Student t distributions are commonly used. In this paper, we shall be concerned only to model heavy-tailed, skewed errors and absence of variance homogeneity with two regression structures based on the skew t distribution. We consider a classic analysis for the parameters of the proposed model. We perform a diagnostic analysis based on global influence and quantile residuals. For different parameter settings and sample sizes, various simulation results are obtained and compared to evaluate the performance of the skew t regression. Further, we illustrate the usefulness of the new regression by means of a real data set (amount of potassium in different soil areas) from a study carried out at the Department of Soil Science of the Luiz de Queiroz School of Agriculture, University of São Paulo.