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Sequential sufficient dimension reduction for large p , small n problems
Author(s) -
Yin Xiangrong,
Hilafu Haileab
Publication year - 2015
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12093
Subject(s) - dimension (graph theory) , reduction (mathematics) , simple (philosophy) , sufficient dimension reduction , dimensionality reduction , task (project management) , computer science , line (geometry) , algorithm , matrix (chemical analysis) , covariance , mathematics , mathematical optimization , combinatorics , statistics , artificial intelligence , philosophy , materials science , geometry , management , epistemology , economics , composite material
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.