Statistics and Its Interface

Volume 1 (2008)

Number 1

Statistical methods with varying coefficient models

Pages: 179 – 195



Jianqing Fan (Department of Operations Research and Financial Engineering, Princeton University, Princeton, N.J., U.S.A.)

Wenyang Zhang (Department of Mathematical Sciences, University of Bath, England, United Kingdom)


The varying coefficient models are very important tool to explore the dynamic pattern in many scientific areas, such as economics, finance, politics, epidemiology, medical science, ecology and so on. They are natural extensions of classical parametric models with good interpretability and are becoming more and more popular in data analysis. Thanks to their flexibility and interpretability, in the past ten years, the varying coefficient models have experienced deep and exciting developments on methodological, theoretical and applied sides. This paper gives a selective overview on the major methodological and theoretical developments on the varying coefficient models.


varying coefficient models, local linear modelling, bandwidth selection, cross-validation, confidence band, hypothesis test, semivarying coefficient models, exponential family, generalized varying coefficient models, local maximum likelihood, nonlinear time series, longitudinal data analysis, Cox models, local partial likelihood

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