Função variância em modelos de regressão não-paramétrica: estimação e usos

Abstract

The technique of linear regression analysis is widely used in real problems. However, when the assumptions necessary for the model are not satisfied, or when the relationship between the predictor and the dependent variable is not linear, we have serious difficulties in using the model. In such cases the use of nonparametric approaches is more appropriate. In this work, we evaluate the performance of the technique of nonparametric regression using kernel estimator and we study specially the case on which the variance is not constant (heteroscedastic model). We focus on the studying of the estimator for the variance proposed by Chen, Cheng e Peng (2009). We also study a measure to evaluate the quality of the kernel estimator of the regression function. This measure, which is the coefficient of determination, was introduced by Huang e Cheng (2008).