<p>The purpose of regression diagnostic techniques is to detect the impact on regression estimates due to violations of assumptions. Robust estimation is frequently applied when there are outliers in data. Least squares estimates are attenuated by presence of outliers in data as outliers lead to inflation of variance estimates. Ridge estimation is used when there is severe multicollinearity among explanatory variables. Also, all classical estimation methods such as ordinary least squares give inconsistent results when the number of explanatory variables exceeds sample size. In this paper we propose a new estimator (SH estimator) that combines Least Absolute Shrinkage and Selection Operation (LASSO), ridge estimator and robust M-estimator to treat the problems of regression such as high dimension, outliers and multicollinearity. Simulation study has been performed with sample sizes (20, 30, 40, 50, 70, 90, 100, 120, 140) and the numbers of explanatory variables (50, 100, 150). Error term has been generated by Cauchy and Normal distributions to study the performance of suggested method. It is shown that the suggested estimator (SH estimator) is superior to ridge estimator, LASSO and M estimator in terms of mean-square error (MSE) criteria.</p>