Estimation and diagnostic analysis in skew-generalized-normal regression models

ABSTRACT

The skew-generalized-normal distribution [Arellano-Valle, RB, Gómez, HW, Quintana, FA. A new class of skew-normal distributions. Comm Statist Theory Methods 2004;33(7):1465–1480] is a class of asymmetric normal distributions, which contains the normal and skew-normal distributions as special cases. The main virtues of this distribution is that it is easy to simulate from and it also supplies a genuine expectation–maximization (EM) algorithm for maximum likelihood estimation. In this paper, we extend the EM algorithm for linear regression models assuming skew-generalized-normal random errors and we develop a diagnostics analyses via local influence and generalized leverage, following Zhu and Lee's approach. This is because Cook's well-known approach would be more complicated to use to obtain measures of local influence. Finally, results obtained for a real data set are reported, illustrating the usefulness of the proposed method.

KEYWORDS:

• Shape parameter
• skewness
• leverage
• local influence
• EM-algorithm

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Clécio S. Ferreira http://orcid.org/0000-0002-7820-1350