WIAS Preprint No. 190, (1995)

Semiparametric single index versus fixed link function modelling


  • Härdle, Wolfgang
  • Sperlich, Stefan
  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2010 Mathematics Subject Classification

  • 62G10 62G07 62H99 62G20 62P20


  • discrete choice models, nonparametric regression, single index modelling, semiparametric alternative, parametric hypothesis, rate-optimal, power function




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. It is therefore interesting to decide between approaches. Here we propose a test of semiparametric versus parametric single index modelling. Our procedure allows that the (linear) index of the semiparametric alternative is different from that of the parametric hypothesis. The test is proved to be rate-optimal in the sense that it provides the (rate) minimal distance between hypothesis and alternative for a given power function.

Appeared in

  • Ann. Statist., 27 (1997), no. 1, pp. 212-243

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