Empirical Performance of Nonparametric Regression with Heteroscedasticity

Abstract

Heteroscedasticity is a well-known violation of an assumption in parametric regression analysis. In such cases, to handle this problem, a generalized least squares method is used. In this article, we have manifested the robustness of nonparametric regression in the case of heteroscedastic errors. Nonparametric regression is a robust method that proceeds without requiring inflexible assumptions from the model.  We empirically compared the performance of the generalized least squares method with multivariate nonparametric kernel regression. Multivariate nonparametric kernel regression is used with a Gaussian kernel and six bandwidths on China's per capita consumption expenditure. The performance of nonparametric regression with Bayesian bandwidth was found better on the basis of mean squared error. Simulation results are also presented, with their graphical representation, where nonparametric regression with different bandwidths at different heteroscedastic levels is observed, and we found that our proposed method performed best in both presence and absence of homoscedasticity.