Leverage effects on Robust Regression Estimators

Abstract

In this study, we assess the performance of some robust regression methods. These are the least- trimmed squares estimator (LTSE), Huber maximum likelihood estimator (HME), S-Estimator (SE) and modified maximum likelihood estimator (MME) which are compared with the ordinary least squares Estimator (OLSE) at different levels of leverages in the predictor variables. Anthropometric data from Komfo Anokye Teaching Hospital (KATH) was used and the comparison is done using root mean square error (RMSE), relative efficiencies (RE), coefficients of determination (R-squared) and power of the test. The results show that robust methods are as efficient as the OLSE if the assumptions of OLSE are met. OLSE is affected by low and high percentage of leverages, HME broke-down with leverages in data. MME and SE are robust to all percentage of aberrations, while LTSE is slightly affected by high percentage leverages perturbation. Thus, MME and SE are the most robust methods, while OLSE and HME are the least robust and the performance of the LTSE is affected by higher percentages of leverage in this study.

Keywords: Leverages, estimators, power of the test, coefficient of determination, root mean square error