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 for the statistical properties of the estimators, but the focus is on the on the 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 examine them with different correlation points/levels and different error distributions with different sample sizes. We concluded that if errors are correlated, then the distribution of errors is important with correlation structures, but correlation points/levels have a less significant effect, comparatively. When errors are uniformly distributed, AMSE is the smallest, followed by any other distribution, and if errors follow the Laplace distribution, then AMSE is the largest, followed by other distributions. Laplace also has some alarming effects. More specifically, the kernel estimator is robust in the case of a simple correlation structure, and AMSEs attain their minimum when errors are uncorrelated.