A Modified M-estimator for the Detection of Outliers

A new P-function is proposed in the family of smoothly redescending M-estimators. The Shi-function associated with this new P-function attains much more linearity in its central section before it redescends, compared to other P-functions such as those of Andrews sine, Tukey’s biweight and Qadir’s beta function resulting in its enhanced efficiency. The iteratively reweighted least squares (IRLS) method based on the proposed Ï-function clearly detects outliers and ignoring those outliers refines the subsequent analysis. Three examples selected from the relevant literature, are used for illustrative purposes. A comparative simulation study has been conducted to evaluate its general applications. The proposed weighted least squares (WLS) method indeed achieves the goals for which it is constructed, for it gives quite improved results in all situations and is able to withstand substantial amount of outliers