The impact of adjusting turning constant of bisquare psi function on some robust estimators in the presence of outliers

Abstract

Turning constant value is often used in practice to provide resistance of outlying data in regression model. Outliers which arise from bad data points may have unduly effect on regression estimators. The influence of outliers cannot be removed or reduced by simply transforming the data using known transformation such as logarithmic transformation. This paper, proposed to examine the impact for adjusting a turning constant value of robust S-estimator, robust M- estimator and robust MM estimators in the presence of outliers in regression model using a Bisquare redescent weighted function. The turning constant value of each estimator will be adjusted by simple modification of increasing or reducing the value to improve the resistant of robust estimators on outlying data. Simulation study was used to compare the performance of the robust methods with adjusting a turning constant value on different sample size. The result of the study showed that increasing or decreasing the turning constant values have significant impact on S- estimators and M estimators on the resistant of outliers. The result also disclosed that, adjusting the turning constant value for MM-estimator will not affect the resistant to outlying data.  The study recommends to use smaller value of turning constant for M-estimation to have more resistance against outlying observations in the regression models. Secondly the study also recommended using a value greater than the default K value for the S-estimation against outlying observations.