Estimation in additive models with highly or nonhighly correlated covariates

Details Estimation in additive models with highly or nonhighly correlated covariates Estimation in additive models with highly or nonhighly correlated covariates

2010-10-02

arxiv.org/abs/1010.0320v1

Annals of Statistics 2010, Vol. 38, No. 3, 1403-1432

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/09-AOS753 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/09-AOS753

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.

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