Performance of the ordinary least squares estimator method of estimating regression parameters and some robust regression methods

Abstract

Background/Objectives: Ordinary least squares (OLS) estimation of regression parameters is a popular technique. It is susceptible to outliers and high-leverage spots in the data, though. A set of methods known as robust regression methods are less susceptible to the impact of outliers and high-leverage points. This study evaluated the performance of the Ordinary Least Squares Estimator (OLSE) method of estimating regression parameters and some robust regression methods. The Least-Trimmed Squares Estimator (LTSE), Huber Maximum likelihood Estimator (HME), S-Estimator (SE) and Modified Maximum likelihood Estimator (MME) were considered in this study. Design/Methods: Criteria for the comparison were: coefficients and their standard errors, relative efficiencies, Root Mean Square Errors, coefficients of determination and the power of the test. The sensitivity of these robust methods were considered using Anthropometric data from Olabisi Onabanjo University Teaching Hospital in Sagamu, Ogun state. The dataset was on Total Body fat and Body Mass Index, Triceps skin-fold, Arm Fat as percent composition of the body and Height as predictors. Leverages were introduced first into two variables, and into all predictors. Results/Conclusion: Results showed that robust methods are as efficient as the OLSE if the assumptions of OLSE are met. Keywords: Ordinary Least Squares (OLS); Robust regression; Least-trimmed squares (LTS); Huber maximum likelihood estimation (HME); S-estimation (SE)