## Relatório de pesquisa 15/09

Nonlinear Regression Models Based on Scale Mixtures of Skew-Normal Distributions, Aldo M. Garay, Víctor H. Lachos and C.A. Abanto-Valle, submitted June 02, 2009.

Abstract

An extension of some standard likelihood based procedures to
nonlinear regression models under scale mixtures of skew-normal
distributions is developed. This novel class of models
provides a useful generalization of the symmetrical nonlinear
regression models since the error distributions cover both skewness and
heavy-tailed distributions such as the skew-t, skew-slash and the
skew-contaminated normal distributions. The main advantage of these
class of distributions is that they have a nice hierarchical
representation which allows easy implementation of inference. A
simple EM-type algorithm for iteratively computing maximum likelihood
estimates is presented and the observed information matrix for
obtaining the asymptotic covariance matrix is derived
analytically. With the aim of identifying atypical observations and/or
model misspecification a brief discussion of the standardized residuals
is given. Finally, an illustration of the methodology is given
considering a data set previously analyzed under skew-normal nonlinear
regression models. Our analysis indicates that a skew-t nonlinear
regression model with 3 degrees of freedom seems to fit the data better
than the skew-normal nonlinear regression model as well as other
asymmetrical nonlinear models in the sense of robustness against
outlying observations.

Mathematics Subject Classifications
(2000):

Keywords: EM algorithm; Skew-normal distribution; Scale mixtures of skew-normal distributions; Nonlinear regression models.

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June 02, 2009

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