Structure adaptive approach for dimension reduction. (English) Zbl 1043.62052

Hristache, Marian; Juditsky, Anatoli; Polzehl, Jörg; Spokoiny, Vladimir

Ann. Stat. 29, No. 6, 1537-1566 (2001).

Summary: 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.

MSC:

62H12	Estimation in multivariate analysis
62G05	Nonparametric estimation
62G20	Asymptotic properties of nonparametric inference
65C60	Computational problems in statistics (MSC2010)

Keywords:

average derivative estimation; structural adaptation