Robust Variables Selection via the Reciprocal Lasso with an Exponential Squared Loss Function

Abstract

Variable selection procedures in regression models have gained increasing attention. They can be used to perform variable selection and are expected to yield accurate estimates. However, there are a number of assumptions in regression models and one of them related with assuming the normal distribution for the error term. The variables  selection methods are not robust to outliers. One of the variables selection methods is the rLasso and it is not robust to outliers. A method has been proposed to make rLasso robust to variable selection by relying on an exponential squared loss function instead of the least squares loss function, which is sensitive to outliers. The effectiveness of the proposed method, which is robust to outliers in X and Y, has been demonstrated through simulations and real data.In this paper, we propose robust  penalized regression estimator based on an exponential squared  loss function, the motivation behind this proposal is that it enables us to introduce robust variable selection method. performance is outperforms the exsisting methods when the outliers are founded. Specifically, under different setting. We conducted simulation studies to compare our proposed method with some existing methods. Our simulation study shows that the proposed method performs well in terms of mean square error and average number of zero coefficients in the presence of significant outliers.