Comparing the Estimation Methods of OLS , LMS and LAD by Proposed Model Selection Criteria for Contaminated Data

Usual estimation of regression coefficients may fail completely if the data contains outliers. In case of contaminated data comparing the methods of ordinary least square (OLS), least median square (LMS) and least absolute deviation (LAD) by traditional model selection criteria gives the misleading conclusion. Outliers are responsible for inflated residual sum of squares (RSS) that results incorrect solution of estimation and test of regression coefficients. We propose weighted residual sum of squares (WRSS) to avoid such inflated problem. Based on WRSS least median of squares (LMS) and least absolute deviations (LAD) estimator performs better than ordinary least squares (OLS) estimator.