Journal of Advanced Research in Applied Mechanics ISSN (online): 2289-7895 | Vol. 8, No. 1. Pages 13-31, 2015 13 Penerbit Akademia Baru Performance of Robust Wild Bootstrap Estimation of Linear Model in the Presence of Outliers and Heteroscedasticity Errors R. Adnan *,1,a , B. A. Rasheed 1,b , S. E. Saffari 2,c and K. D. Pati 1,d 1 Department of mathematics, Faculty of Science, UTM, 81310 UTM Skudai, Johor, Malaysia 2 Centre of Education, Sabzevar University of Medical Sciences, Sabzevar, Iran. a,* robiah@utm.my, b arasheedbello@yahoo.com, c ehsanreiki@yahoo.com, d kafi_dano@yahoo.com Abstract- Bootstrap techniques are widely used today in many other fields such as economics, Business Administration, Physics, Engineering, Chemistry, Meteorological, Biological Sciences and Medicine. This paper is concerned with the estimation of linear regression model parameters in the presence of heteroscedasticity using wild bootstrap approaches of Wu and Liu. The empirical evidence has shown that these techniques are effective in the presence of heteroscedasticity. However, when there are outliers in the data, this method is no longer effective. To overcome this situation, this paper proposed robust wild bootstrap estimation methods where heteroscedasticity and outliers occur simultaneously. The proposed method is based on the Tukey-redesceding M-estimator which incorporate the LTS and LMS estimator, robust scale and location, and the wild bootstrap sampling procedures of Liu and Wu. Its performance is compared with other existing robust wild bootstrap estimator of MM-estimator using real data and simulation study. The results obtained from this study disclosed that the proposed methods offer a substantial improvement over the existing techniques and proved to be a good alternative estimator. Copyright © 2015 Penerbit Akademia Baru - All rights reserved. Keywords: Robust Estimation, Wild Bootstrap, Bias, Standard error and RMS. 1.0 INTRODUCTION: Wild bootstrap method was first proposed by [1] which gives a better performance for homoscedastic and heteroscedastic models. However, a better alternative estimation method is introduced by [2-3] following the idea of [1] to estimate the regression model parameters. The most common bootstrap methods are the residuals bootstrap and the paired bootstrap which are defined in [4], and some of their asymptotic properties can be found in [5-7] among others. For bootstrap method, [8] proposed a bootstrap procedure based on random weight on the loss functions, [9] established a modified form of the residuals bootstrap, and [10] considered the validity of paired bootstrap techniques. [11] proposed a modified weighted bootstrap estimation method based on LTS. To account for heteroscedasticity [1-3] proposed the wild bootstrap techniques by randomly weighting the residuals. However, different attempts have been made to use the procedure of [1-2] wild bootstrap techniques to remedy the problem of heteroscedasticity error variance. Others including [12], [13-15] have considered the properties of wild bootstrap, but the existing theories of wild bootstrap are all based on ordinary least squares (OLS) method they can be seriously affected in the presence