On directional regression for dimension reduction

Bing Li, Shaoli Wang

Research output: Contribution to journalArticlepeer-review

242 Scopus citations

Abstract

We introduce directional regression (DR) as a method for dimension reduction. Like contour regression, DR is derived from empirical directions, but achieves higher accuracy and requires substantially less computation. DR naturally synthesizes the dimension reduction estimators based on conditional moments, such as sliced inverse regression and sliced average variance estimation, and in doing so combines the advantages of these methods. Under mild conditions, it provides exhaustive and √n-consistent estimate of the dimension reduction space. We develop the asymptotic distribution of the DR estimator, and from that a sequential test procedure to determine the dimension of the central space. We compare the performance of DR with that of existing methods by simulation and find strong evidence of its advantage over a wide range of models, Finally, we apply DR to analyze a data set concerning the identification of hand-written digits.

Original languageEnglish (US)
Pages (from-to)997-1008
Number of pages12
JournalJournal of the American Statistical Association
Volume102
Issue number479
DOIs
StatePublished - Sep 2007

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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