Average regression surface for dependent data

Zongwu Cai, Jianqing Fan

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We study the estimation of the additive components in additive regression models, based on the weighted sample average of regression surface, for stationary α-mixing processes. Explicit expression of this method makes possible a fast computation and allows an asymptotic analysis. The estimation procedure is especially useful for additive modeling. In this paper, it is shown that the average surface estimator shares the same optimality as the ideal estimator and has the same ability to estimate the additive component as the ideal case where other components are known. Formulas for the asymptotic bias and normality of the estimator are established. A small simulation study is carried out to illustrate the performance of the estimation and a real example is also used to demonstrate our methodology.

Original languageEnglish (US)
Pages (from-to)112-142
Number of pages31
JournalJournal of Multivariate Analysis
Issue number1
StatePublished - Oct 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


  • Additive models
  • Asymptotic bias
  • Asymptotic normality
  • Kernel estimates
  • Local linear estimate
  • α-mixing


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