Semiparametric single index versus fixed function modelling. The Annals of Statistics

Discrete choice models are frequently used in statistical and econo-metric practice. Standard models such as logit models are based on exact knowledge of the form of the link and linear index function. Semiparamet-ric models avoid possible misspeci®cation but often introduce a computa-tional burden especially when optimization over nonparametric and parametric components are to be done iteratively. It is therefore interest-ing to decide between approaches. Here we propose a test of semiparamet-ric 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. 1. Introduction. Discret