Structure adaptive approach for dimension reduction

Marian Hristache, Anatoli Juditsky, Jörg Polzehl, Vladimir Spokoiny

Research output: Contribution to journalArticlepeer-review

100 Citations (Scopus)

Abstract

We propose a new method of effective dimension reduction for a multi-index model which is based on iterative improvement of the family of average derivative estimates. The procedure is computationally straightforward and does not require any prior information about the structure of the underlying model. We show that in the case when the effective dimension m of the index space does not exceed 3, this space can be estimated with the rate n-1/2 under rather mild assumptions on the model.

Original languageEnglish
Pages (from-to)1537-1566
Number of pages30
JournalAnnals of Statistics
Volume29
Issue number6
DOIs
Publication statusPublished - Dec 2001
Externally publishedYes

Keywords

  • Average derivative estimation
  • Dimension-reduction
  • Index space
  • Multi-index model
  • Structural adaptation

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