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March, 1993 Optimal Smoothing in Single-Index Models
Wolfgang Hardle, Peter Hall, Hidehiko Ichimura
Ann. Statist. 21(1): 157-178 (March, 1993). DOI: 10.1214/aos/1176349020


Single-index models generalize linear regression. They have applications to a variety of fields, such as discrete choice analysis in econometrics and dose response models in biometrics, where high-dimensional regression models are often employed. Single-index models are similar to the first step of projection pursuit regression, a dimension-reduction method. In both cases the orientation vector can be estimated root-n consistently, even if the unknown univariate function (or nonparametric link function) is assumed to come from a large smoothness class. However, as we show in the present paper, the similarities end there. In particular, the amount of smoothing necessary for root-n consistent orientation estimation is very different in the two cases. We suggest a simple, empirical rule for selecting the bandwidth appropriate to single-index models. This rule is studies in a small simulation study and an application in binary response models.


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Wolfgang Hardle. Peter Hall. Hidehiko Ichimura. "Optimal Smoothing in Single-Index Models." Ann. Statist. 21 (1) 157 - 178, March, 1993.


Published: March, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0770.62049
MathSciNet: MR1212171
Digital Object Identifier: 10.1214/aos/1176349020

Primary: 62H99
Secondary: 62H05

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.21 • No. 1 • March, 1993
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