Estimation in additive models with highly or nonhighly correlated covariates

Jiancheng Jiang, Yingying Fan, Jianqing Fan

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1403-1432
Number of pages30
JournalAnnals of Statistics
Volume38
Issue number3
DOIs
StatePublished - Jun 2010

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Additive model
  • Backfitting
  • Local linear smoothing
  • Normalization
  • Varying coefficient

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