Two cross-validation criteria for SIR\({}_\alpha\) and PSIR\({}_\alpha\) methods in view of prediction
type: Item
instance of: scholarly article
title: Two cross-validation criteria for SIR\({}_\alpha\) and PSIR\({}_\alpha\) methods in view of prediction
zbMATH Open document ID: 1050.62044
DOI: 10.1007/BF03354618
author: Ali Gannoun
author: Jérôme Saracco
published in: Computational Statistics
publication date: 2004-11-24T00:00:00Z
review text: The sliced inverse regression technique SIR and its ``robustified'' version PSIR for fitting the single-index regression model \(y=f(x^\top\beta,\varepsilon)\) are considered. (Here \(f\) is an unknown link function to be estimated nonparametrically, \(x^\top\beta\) is the index.) The authors discuss the mixed SIR-I and SIR-II method, called SIR\({}_\alpha\) and PSIR\({}_\alpha\). Cross-validation criteria for the choice of the mixing parameter \(\alpha\) and the bandwidth in the Nadaraya-Watson estimator for \(f\) are proposed. Simulation results are presented for the model \(y=10+(x^\top\beta +C)^2+\varepsilon\), with \(x\) having standard Gaussian distribution in \(R^5\).
Mathematics Subject Classification ID: 62G08
Mathematics Subject Classification ID: 62G09
zbMATH DE Number: 2118522
zbMATH Keywords: sliced inverse regression
zbMATH Keywords: bandwidth selection
zbMATH Keywords: Nadaraya-Watson estimator
zbMATH Keywords: mixed SIR
zbMATH Keywords: single index regression
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2118522