Direct estimation of the index coefficient in a single-index model

• 成果类型: Article
• 署名作者: Hristache, M; Juditsky, A; Spokoiny, V
• 署名单位: Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI); Institut Polytechnique de Paris; ENSAE Paris; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2001
• 页码: 595-623
• 关键词: projection pursuit regression; semiparametric estimation

摘要

Single-index modeling is widely applied in, for example, econometric studies as a compromise between too restrictive parametric models and flexible but hardly estimable purely nonparametric, models. By such modeling the statistical analysis usually focuses on estimating the index coefficients. The average derivative estimator (ADE) of the index vector is based on the fact that the average gradient of a single index function f(x(T)beta) is proportional to the index vector beta. Unfortunately, a straightforward application of this idea meets the so-called curse of dimensionality problem if the dimensionality d of the model is larger than 2. However, prior information about the vector beta can be used for improving the quality of gradient estimation by extending the weighting kernel in a direction of small directional derivative. The method proposed in this paper consists of such iterative improvements of the original ADE. The whole procedure requires at most 2 log n iterations and the resulting estimator is rootn-consistent under relatively mild assumptions on the model independently of the dimensionality d.