SAVE: Robust or not?

Abstract

Sliced average variance estimation (SAVE) is one of the best methods for estimating central dimension-reduction subspace in semi parametric regression models when covariates are normal. In recent days SAVE is being used to analyze DNA microarray data especially in tumor classification but most important drawback is normality of covariates. In this article, the asymptotic behavior of estimates of CDR space under varying slice size is studied through simulation studies when covariates are non normal but follows linearity condition as well as when covariates slightly perturbed from normal distribution and we observed that serious error may occur under violation normality assumption.

Keywords:

• Central dimension-reduction subspace
• Convergence rate
• Dimension determination
• Mixture distribution
• Slice average variance estimation