Robust Sparse Sufficient Dimension Reduction via Adaptive Lasso Penalty

In some multi-index models applications, there is an important role for dimension reduction and variable selection (VS) methods. The ALMAVE is a method for variables selection under sufficient dimension reduction theory settings. It combines the adaptive Lasso and MAVE (minimum average variance estimation) to produce sparse and accurate solutions. The ALMAVE is a very sensitive method to outliers in the response y due to use the least-squares criterion. In this article, we proposed robust ALMAVE. Also, an efficient estimation algorithm was proposed. The simulation studies and Logo design data analysis were employed to check the effectiveness of ALMAVE.