Comparisons of Hampel and Andrews sin PSI function for heteroscedasticity model in the presence of outliers and multicollinearity

Abstract

The presence of heteroscedasticity, multicollinearity and outliers are classical problems of data within the linear regression framework. This research is a proposal of new methods which can be a potential candidate for weighted robust wild bootstrap regression as well as the multicollinearity robust regression model with outliers’ pattern based on Latin root. This proposal arises as a logical combination of principles used in the Latin root, wild bootstrap sampling procedure of Wu and Liu. The weighted robust GM-estimator of Krasker and Welsch (1982) with initial MM-estimator of Yohai (1987) and S-estimator of Rousseeuw and Yohai (1984) together with two different weighting procedures of Hampel’s and Andrews sin weighted function are considered in the analysis. This paper investigate the nonresistance of weighted robust wild bootstrap (WRW Boot) regression and our proposed method for resistance to multicollinearity, outliers and heteroscedasticity error variance. The use of modified weighted robust wild bootstrap methods (WRW Boot) based on Latin root with multicollinearity and outlier diagnostic method yields more reliable trend estimations. From numerical example and simulation study, the resulting of the modified weighted robust wild bootstrap methods based on Latin root with multicollinearity and outlier diagnostic method (WRW Boot) is efficient than other estimators, using Standard Error (SE) and the Root Mean Squared Error criterion for numerical example and simulation study respectively for many combinations of error distribution and degree of multicollinearity.