INFERENCE FOR SINGLE-INDEX QUANTILE REGRESSION MODELS WITH PROFILE OPTIMIZATION

• 成果类型: Article
• 署名作者: Ma, Shujie; He, Xuming
• 署名单位: University of California System; University of California Riverside; University of Michigan System; University of Michigan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1404
• 发表日期: 2016
• 页码: 1234-1268
• 关键词: nonconcave penalized likelihood; variable selection; smoothing splines; asymptotics; estimators; Lasso

摘要

Single index models offer greater flexibility in data analysis than linear models but retain some of the desirable properties such as the interpretability of the coefficients. We consider a pseudo-profile likelihood approach to estimation and testing for single-index quantile regression models. We establish the asymptotic normality of the index coefficient estimator as well as the optimal convergence rate of the nonparametric function estimation. Moreover, we propose a score test for the index coefficient based on the gradient of the pseudo-profile likelihood, and employ a penalized procedure to perform consistent model selection and model estimation simultaneously. We also use Monte Carlo studies to support our asymptotic results, and use an empirical example to illustrate the proposed method.