Local composite quantile regression smoothing: an efficient and safe alternative to local polynomial regression

• 成果类型: Article
• 署名作者: Kai, Bo; Li, Runze; Zou, Hui
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2009.00725.x
• 发表日期: 2010
• 页码: 49-69
• 关键词: Bandwidth

摘要

Local polynomial regression is a useful non-parametric regression tool to explore fine data structures and has been widely used in practice. We propose a new non-parametric regression technique called local composite quantile regression smoothing to improve local polynomial regression further. Sampling properties of the estimation procedure proposed are studied. We derive the asymptotic bias, variance and normality of the estimate proposed. The asymptotic relative efficiency of the estimate with respect to local polynomial regression is investigated. It is shown that the estimate can be much more efficient than the local polynomial regression estimate for various non-normal errors, while being almost as efficient as the local polynomial regression estimate for normal errors. Simulation is conducted to examine the performance of the estimates proposed. The simulation results are consistent with our theoretical findings. A real data example is used to illustrate the method proposed.