Sequential sufficient dimension reduction for largep, smallnproblems
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2015 · Volume 77 · Issue 4
Abstract
We propose a new and simple framework for dimension reduction in the largep, smallnsetting. The framework decomposes the data into pieces, thereby enabling existing approaches forn>pto be adapted ton<pproblems. 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.
Keywords
Central subspace, High dimensional data, Largep, smalln, Sufficient dimension reduction, Sufficient variable selection
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