Quantile regression with varying coefficients

• 成果类型: Article
• 署名作者: Kim, Mi-Ok
• 署名单位: Cincinnati Children's Hospital Medical Center; University System of Ohio; University of Cincinnati; University of Kentucky
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000966
• 发表日期: 2007
• 页码: 92-108
• 关键词: Nonparametric regression; conditional quantiles; polynomial splines; smoothing splines; median regression; longitudinal data; models; estimators; intervals

摘要

Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider conditional quantiles with varying coefficients and propose a methodology for their estimation and assessment using polynomial splines. The proposed estimators are easy to compute via standard quantile regression algorithms and a stepwise knot selection algorithm. The proposed Rao-score-type test that assesses the model against a linear model is also easy to implement. We provide asymptotic results on the convergence of the estimators and the null distribution of the test statistic. Empirical results are also provided, including an application of the methodology to forced expiratory volume (FEV) data.