Modelos de regressão PLS com erros heteroscedásticos

Abstract

Two problems related to Partial Least Squares method are considered in this work. Heteroscedastic errors and an asymmetrical error distribution. In the _rst part of this work a methodology is developed which allows, based in PLS methods, to estimate the model parameters in the presence of non-constant error variance. This technique is compared with the usual PLS method which considers homoscedastic erros. The PLS method is an distribution free approach, that is, it does not assume any distribution for the error terms. In order to estimate the heterocedastic structure an probability distribution is attributed to the errors, similar to the idea of Bastien et al: (2005). In this work, it is proposed a class of asymmetric distributions, the asymmetric normal distribution, presented in Azzalini (1985), which includes the normal distribution as a particular case. For the heteroscedasticity detection is proposed adaptations of the White test, the Goldfeld-Quandt test and an test proposed by Xei et al: (2009), which is used for testing the homogeneity of the scale parameter and/or signi_cance of autocorrelation in skew-normal nonlinear regression model. The test methods are illustrated with two numerical examples. All the methods present in the work are illustrated with simulated and real datasets.