Impact analysis of correlated and non-normal errors in nonparametric regression estimation: A simulation study

Abstract

In nonparametric regression, the correlation of errors can have important consequences on the statistical properties of the estimators, but the focus is identification of the effect on Average Mean Squared Error (AMSE). This is performed by a Monte Carlo experiment where we use two types of correlation structures and examined with different correlation points/levels and different error distributions with different sample sizes. We concluded that if errors are correlated then distribution of error is important with correlation structures but correlation points/levels have a less significant effect, comparatively. When errors are uniformly distributed, then AMSE are smallest then any other distribution and if errors follow the Laplace distribution then AMSE are largest then other distributions also Laplace have some alarming effect. More keenly, kernel estimator is robust in case of simple correlation structure, and AMSEs attains their minimum when errors are uncorrelated.