Estimating multi-index models with response-conditional least squares
type: Item
instance of: scholarly article
title: Estimating multi-index models with response-conditional least squares
zbMATH Open document ID: 1472.62043
DOI: 10.1214/20-EJS1785
author: Timo Klock
author: Alessandro Lanteri
author: Stefano Vigogna
published in: Electronic Journal of Statistics
publication date: 2021-08-09T00:00:00Z
full work available at URL: https://arxiv.org/abs/2003.04788
review text: In the general area of sufficient dimension reduction, a novel methodology is derived and analyzed for estimation of the index space \(A\) of a high dimensional multi-index regression model \(E(Y|X) = g(A^T X)\) with \(g\) being a link function. The estimation method is based on the solution of localized least squares problems and uses the span of linear regression slope coefficients computed over level sets of the data. The propagation error of the index space estimate in the regression of the link function is studied in detail. The proposed method is shown to be attractive to practitioners by being computationally efficient and easy to implement as only one hyperparameter (the number of level sets) needs to be specified. Furthermore, finite sample generalization bounds for the regression model are provided which account for the projection error; in turn the bounds are used in quantifying the generalization bound for derived regression estimate and obtain that when response-conditional least squares are paired with piecewise polynomial regression, this leads to optimal estimation of the multi-index model.
reviewed by: Dimitrios Bagkavos
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62G08
Mathematics Subject Classification ID: 62H12
zbMATH DE Number: 7379656
zbMATH Keywords: multi-index model
zbMATH Keywords: sufficient dimension reduction
zbMATH Keywords: nonparametric regression
zbMATH Keywords: finite sample bounds
describes a project that uses: simest
MaRDI profile type: Publication
arXiv ID: 2003.04788
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description: scientific article