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.
Publié le : 2001-12-14
Classification:
Dimensioin-reduction,
multi-index model,
index space,
average derivative estimation,
structural adaptation,
62G05,
62H40,
62G20
@article{1015345954,
author = {Hristache, Marian and Juditsky, Anatoli and Polzehl, J\"org and Spokoiny, Vladimir},
title = {Structure Adaptive Approach for Dimension Reduction},
journal = {Ann. Statist.},
volume = {29},
number = {2},
year = {2001},
pages = { 1537-1566},
language = {en},
url = {http://dml.mathdoc.fr/item/1015345954}
}
Hristache, Marian; Juditsky, Anatoli; Polzehl, Jörg; Spokoiny, Vladimir. Structure Adaptive Approach for Dimension Reduction. Ann. Statist., Tome 29 (2001) no. 2, pp. 1537-1566. http://gdmltest.u-ga.fr/item/1015345954/