ESTIMATION IN ADDITIVE MODELS WITH HIGHLY OR NONHIGHLY CORRELATED COVARIATES

• 成果类型: Article
• 署名作者: Jiang, Jiancheng; Fan, Yingying; Fan, Jianqing
• 署名单位: University of North Carolina; University of North Carolina Charlotte; University of Southern California; Princeton University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS753
• 发表日期: 2010
• 页码: 1403-1432
• 关键词: local polynomial regression; 2-way semilinear model; cdna microarray data; asymptotic properties; normalization

摘要

Motivated by normalizing DNA microarray data and by predicting the interest rates, we explore nonparametric estimation of additive models with highly correlated covariates. We introduce two novel approaches for estimating the additive components, integration estimation and pooled backfitting estimation. The former is designed for highly correlated covariates, and the latter is useful for nonhighly correlated covariates. Asymptotic normalities of the proposed estimators are established. Simulations are conducted to demonstrate finite sample behaviors of the proposed estimators, and real data examples are given to illustrate the value of the methodology.