A Comparison of Robust and Nonparametric Estimators Under the Simple Linear Regression Model

Abstract

The present study investigates parameter estimation under the simple linear regression model for situations in which the underlying assumptions of ordinary least squares (OLS) estimation are untenable. Classical nonparametric estimation methods are directly compared against some robust estimation methods for conditions in which varying degrees of outliers are present in the observed data. Additionally, estimator performance is considered under conditions in which the normality assumption regarding error distributions is violated. The study addresses the problem via computer simulation methods. The study design includes three sample sizes (n = 10, 30, 50) crossed with five types of error distributions (unit normal, 10% contaminated normal, 30% contaminated normal, lognormal, t-5df). Variance, bias, mean square error, and relative mean square error are used to evaluate estimator performance.
Recommendations to applied researchers and direction for further study are considered.