LOCAL QUASI-LIKELIHOOD WITH A PARAMETRIC GUIDE

• 成果类型: Article
• 署名作者: Fan, Jianqing; Wu, Yichao; Feng, Yang
• 署名单位: Princeton University; North Carolina State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS713
• 发表日期: 2009
• 页码: 4153-4183
• 关键词: GENERALIZED LINEAR-MODELS; Nonparametric Regression; DENSITY-ESTIMATION; reducing variance; estimators; selection

摘要

Generalized linear models and the quasi-likelihood method extend the ordinary regression models to accommodate more general conditional distributions of the response. Nonparametric methods need no explicit parametric specification, and the resulting model is completely determined by the data themselves. However, nonparametric estimation schemes generally have a slower convergence rate such as the local polynomial smoothing estimation of nonparametric generalized linear models studied in Fan, Heckman and Wand [J. Amer Statist. Assoc. 90 (1995) 141-150]. In this work, we propose a unified family of parametrically-guided nonparametric estimation schemes. This combines the merits of both parametric and nonparametric approaches and enables us to incorporate prior knowledge. Asymptotic results and numerical simulations demonstrate the improvement of our new estimation schemes over the original nonparametric counterpart.