Efficient estimation and inferences for varying-coefficient models

Zongwu Cai, Jianqing Fan, Runze Li

Research output: Contribution to journalArticlepeer-review

362 Scopus citations


This article deals with statistical inferences based on the varying-coefficient models proposed by Hastie and Tibshirani. Local polynomial regression techniques are used to estimate coefficient functions, and the asymptotic normality of the resulting estimators is established. The standard error formulas for estimated coefficients are derived and are empirically tested. A goodness-of-fit test technique, based on a nonparametric maximum likelihood ratio type of test, is also proposed to detect whether certain coefficient functions in a varying-coefficient model are constant or whether any covariates are statistically significant in the model. The null distribution of the test is estimated by a conditional bootstrap method. Our estimation techniques involve solving hundreds of local likelihood equations. To reduce the computational burden, a one-step Newton-Raphson estimator is proposed and implemented. The resulting one-step procedure is shown to save computational cost on an order of tens with no deterioration in performance, both asymptotically and empirically. Both simulated and real data examples are used to illustrate our proposed methodology.

Original languageEnglish (US)
Pages (from-to)888-902
Number of pages15
JournalJournal of the American Statistical Association
Issue number451
StatePublished - Sep 1 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Asymptotic normality
  • Bootstrap
  • Generalized linear models
  • Goodness-of-fit
  • Local polynomial fitting
  • One-step procedure


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