Sequential Sufficient Dimension Reduction for Large p, Small n Problems

Abstract

Summary We propose a new and simple framework for dimension reduction in the large p, small n setting. The framework decomposes the data into pieces, thereby enabling existing approaches for n>p to be adapted to n < p problems. Estimating a large covariance matrix, which is a very difficult task, is avoided. We propose two separate paths to implement the framework. Our paths provide sufficient procedures for identifying informative variables via a sequential approach. We illustrate the paths by using sufficient dimension reduction approaches, but the paths are very general. Empirical evidence demonstrates the efficacy of our paths. Additional simulations and applications are given in an on-line supplementary file.