Robust Multiple Linear Backward EliminationRegression

Abstract

For building a linear prediction model, robust Backward Elimination (RBE) algorithm, which is computationally useful and scalable to high-dimensional large datasets, is introduced in this investigation. Backward Elimination (BE) can be stated in terms of sample correlations and simple RBE can be obtained by swapping out these correlations with their corresponding robust counterparts. The robust correlation for winsorized data was employed based on the adjusted winsorized correlation as a robust bivariate correlation. In another study, the Spearman rank correlation was employed as a robust bivariate correlation. However, the RBE has some drawbacks in the presence of multivariate outliers. In this article, the usage of FastMCD (Fast minimum covariance determinant)-based correlation is proposed in BE to reduce the influence of outlying data points. We call this proposed method BEmcd. A comprehensive simulation study was conducted to evaluate the performance of BEmcd with that of RBE based on winsorized correlation and Spearman rank correlation. Simulations and an application of actual data demonstrate the outstanding performance of BEmcd. Dhaka Univ. J. Sci. 71(2): 134-141, 2023 (July)