Robust PC with wild bootstrap estimation of linear model in the presence of outliers, multicollinearity and heteroscedasticity error variance

Abstract

The regression model estimator is considered efficient if it is robust and resistant to the presence of heteroscedasticity variance, multicollinearity or unusual observations called outliers. However, in regard to these problems, the wild bootstrap and robust wild bootstrap are no longer efficient since they could not produce the smallest variance. Hence this research investigates the use of robust PC with wild bootstrap techniques on regression model as an estimator for real and simulation data in a situation where multicollinearity, heteroscedasticity and multiple outliers are present. This paper proposed a robust procedure based on the weighted residuals which combined the Tukey bisquare weighted function, principal component analysis (PCA) to remedy the multicollinearity problems, least trimmed squares (LTS) estimator, robust location and scale, and the wild bootstrap sampling procedure of Wu and Liu that remedy the heteroscedasticity error variance. RPCWBootWu and RPCWBootLiu were obtained through a modified version of RBootWu and RBootLiu. Finally, based on the real data and simulation study, the performance of the RPCWBootWu and RPCWBootLiu is compared with the existing RBootWu, RBootLiu and also with BootWu, BootLiu using the biased, RMSE and standard error. The numerical example and simulation study shows that the RPCWBootWu and RPCWBootLiu techniques have proven to be a good alternative estimator for regression model with lower standard error values.