Estimation in additive models with highly or nonhighly correlated covariates
Jiancheng Jiang, Yingying Fan, Jianqing Fan
The Annals of Statistics · 2010 · Volume 38 · Issue 3
Abstract
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.
Keywords
60J60, 62G10, 62G20, Additive model, backfitting, local linear smoothing, normalization, varying coefficient
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