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February 1997 Semiparametric single index versus fixed link function modelling
W. Härdle, V. Spokoiny, S. Sperlich
Ann. Statist. 25(1): 212-243 (February 1997). DOI: 10.1214/aos/1034276627


Discrete choice models are frequently used in statistical and econometric practice. Standard models such as logit models are based on exact knowledge of the form of the link and linear index function. Semiparametric models avoid possible misspecification but often introduce a computational burden especially when optimization over nonparametric and parametric components are to be done iteratively. It is therefore interesting to decide between approaches. Here we propose a test of semiparametric versus parametric single index modelling. Our procedure allows the (linear) index of the semiparametric alternative to be different from that of the parametric hypothesis. The test is proved to be rate-optimal in the sense that it provides (rate) minimal distance between hypothesis and alternative for a given power function.


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W. Härdle. V. Spokoiny. S. Sperlich. "Semiparametric single index versus fixed link function modelling." Ann. Statist. 25 (1) 212 - 243, February 1997.


Published: February 1997
First available in Project Euclid: 10 October 2002

zbMATH: 0869.62033
MathSciNet: MR1429923
Digital Object Identifier: 10.1214/aos/1034276627

Primary: 62G10, 62H40
Secondary: 62G20, 62P20

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 1 • February 1997
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