Semiparametric single index versus fixed line function modelling

• 成果类型: Article
• 署名作者: Härdle, W; Spokoiny, V; Sperlich, S
• 署名单位: Humboldt University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 212-243
• 关键词: projection pursuit; regression

摘要

Discrete choice models are frequently used in statistical and econometric practice. Standard models such as legit 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.