WIAS Preprint No. 569, (2000)

Structure adaptive approach for dimension reduction


  • Hristache, Marian
  • Juditsky, Anatoli
  • Polzehl, Jörg
    ORCID: 0000-0001-7471-2658
  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2010 Mathematics Subject Classification

  • 62G05 62H40 62G20


  • dimension-reduction, multi-index model, index space, average derivative estimation, structural adaptation




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.

Appeared in

  • Ann. Statist., 29, no. 6 (2001), pp 1537 - 1566

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