Date of Award

Spring 2021

Document Type

Open Access Thesis


Public Health

First Advisor

Marco Geraci


In this study, we compare ordinary least squares (OLS), generalized least squares (GLS), M- and quantile regression (QR) estimators for a continuous response variable under different scenarios by conducting a simulation study. We assess the performance of the estimators in terms of bias, average distance, mean squared error, coverage probability, and ratio of estimated standard error and empirical standard deviation. OLS estimator performs the best when the errors are homoscedastic normal or homoscedastic but skewed (exponential) having no outliers. GLS estimator shows good comparative results to QR when the errors are heteroscedastic normal or heteroscedastic heavy-tailed (t-distributed). The most satisfactory performance of the M-estimator is revealed when the errors are homoscedastic heavy-tailed with no outliers, and homoscedastic normal or homoscedastic exponential contaminated with outliers. In all of the scenarios with heavy-tailed-skewed (log-normal) errors, the QR estimator is shown to be more accurate and stable than the other estimators. Moreover, as a robust estimator, both M- and QR estimators become more reasonable than the others in scenarios with outliers contaminated errors which is also evident from real data analysis.

Included in

Biostatistics Commons