Adaptive varying-coefficient linear models

Jianqing Fan, Qiwei Yao, Zongwu Cai

Research output: Contribution to journalArticle

141 Scopus citations

Abstract

Varying-coefficient linear models arise from multivariate nonparametric regression, non-linear time series modelling and forecasting, functional data analysis, longitudinal data analysis and others. It has been a common practice to assume that the varying coefficients are functions of a given variable, which is often called an index. To enlarge the modelling capacity substantially, this paper explores a class of varying-coefficient linear models in which the index is unknown and is estimated as a linear combination of regressors and/or other variables. We search for the index such that the derived varying-coefficient model provides the least squares approximation to the underlying unknown multidimensional regression function. The search is implemented through a newly proposed hybrid backfitting algorithm. The core of the algorithm is the alternating iteration between estimating the index through a one-step scheme and estimating coefficient functions through one-dimensional local linear smoothing. The locally significant variables are selected in terms of a combined use of the t-statistic and the Akaike information criterion. We further extend the algorithm for models with two indices. Simulation shows that the methodology proposed has appreciable flexibility to model complex multivariate non-linear structure and is practically feasible with average modern computers. The methods are further illustrated through the Canadian mink-muskrat data in 1925-1994 and the pound-dollar exchange rates in 1974-1983.

Original languageEnglish (US)
Pages (from-to)57-80
Number of pages24
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume65
Issue number1
DOIs
StatePublished - 2003

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Akaike information criterion
  • Backfilling algorithm
  • Generalized cross-validation
  • Local linear regression
  • Local significant variable selection
  • One-step estimation
  • Smoothing index

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