Nonparametric n-1/2-consistent estimation for the general transformation models

• 成果类型: Article
• 署名作者: Ye, JM; Duan, NH
• 署名单位: University of Chicago; RAND Corporation
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 2682-2717
• 关键词: projection pursuit regression; MULTIPLE-REGRESSION

摘要

We propose simple estimators for the transformation function Delta and the distribution function F of the error for the model Delta(Y) = alpha + X beta + epsilon. It is proved that these estimators are consistent and can achieve the unusual n(-1/2) rate of convergence on any finite interval under some regularity conditions. We show that our estimators are more attractive than another class of estimators proposed by Horowitz. Interesting decompositions of the estimators are obtained. The estimator of F is independent of the unknown transformation function Delta, and the variance of the estimator for Delta depends on Delta only through the density function of X. Through simulations, we find that the procedure is not sensitive to the choice of bandwidth, and the computation load is very modest. In almost all cases simulated, our procedure works substantially better than median nonparametric regression.