Robust Wild Bootstrap Method Based on LMS Estimator with Monte Carlo Simulation in the Presence of Heteroscedasticity Error and Outliers

Abstract

Abstract This research applies wild bootstrap techniques to a linear regression model with heteroscedasticity and outliers using Monte-Carlo techniques. For this research, the Monte-Carlo method was applied to generate samples of 120 and 200 observations from random samples of sizes 40 that were duplicated three and five times, respectively. However, the stochastic error for different sampling sizes similarly follows a normal distribution and the linear regression model is based on a fixed X variable for varied sample sizes. The regression model was introduced a form of heteroscedasticity to justify how the parameter estimate performed. By replacing a suitable outlier's observation for a good observation, the outliers are generated. The optimal approach was determined by applying the BootWu, BootLiu, RBootWu, and RBootLiu in the presence of outliers and heteroscedasticity errors. The robust location and scale, the wild bootstrap sampling procedure of Wu's and Liu's, and the Least Median Squares (LMS) estimator were combined with the Alamgir redescending M-estimate weighted function to compare this estimator. Using bias, RMSE, and average standard error, the performance of the proposed methods RWBootWu and RWBootLiu is compared to the performance of the current methods RBootWu, RBootLiu, BootWu, and BootLiu. The simulation study's findings show that RWBootWu and RWBootLiu are good alternatives to existing estimators for regression models. Mathematics Subject Classification 62F35 Robustness and adaptive procedures (parametric inference) 62F40 Bootstrap, jackknife and other resampling methods 62H12 Estimation in multivariate analysis 62J07 Ridge regression; shrinkage estimators (Lasso) 62K25 Robust parameter designs 62K99 None of the above, but in this section