The Annals of Statistics

Semiparametric single index versus fixed link function modelling

S. Sperlich, W. Härdle, and V. Spokoiny

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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.

Article information

Ann. Statist., Volume 25, Number 1 (1997), 212-243.

First available in Project Euclid: 10 October 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G10: Hypothesis testing 62H40
Secondary: 62G20: Asymptotic properties 62P20: Applications to economics [See also 91Bxx]

Semiparametric models single index model hypothesis testing


Härdle, W.; Spokoiny, V.; Sperlich, S. Semiparametric single index versus fixed link function modelling. Ann. Statist. 25 (1997), no. 1, 212--243. doi:10.1214/aos/1034276627.

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