Statistical estimation in varying coefficient models

Jianqing Fan Wenyang Zhang

Statistics Theory and Methods mathscidoc:1912.43254

The annals of Statistics, 27, (5), 1491-1518, 1999
Varying coefficient models are a useful extension of classical linear models. They arise naturally when one wishes to examine how regression coefficients change over different groups characterized by certain covariates such as age. The appeal of these models is that the coef. cient functions can easily be estimated via a simple local regression. This yields a simple one-step estimation procedure. We show that such a one-step method cannot be optimal when different coefficient functions admit different degrees of smoothness. This drawback can be repaired by using our proposed two-step estimation procedure. The asymptotic mean-squared error for the two-step procedure is obtained and is shown to achieve the optimal rate of convergence. A few simulation studies show that the gain by the two-step procedure can be quite substantial. The methodology is illustrated by an application to an environmental data set.
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@inproceedings{jianqing1999statistical,
  title={Statistical estimation in varying coefficient models},
  author={Jianqing Fan, and Wenyang Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113231418926814},
  booktitle={The annals of Statistics},
  volume={27},
  number={5},
  pages={1491-1518},
  year={1999},
}
Jianqing Fan, and Wenyang Zhang. Statistical estimation in varying coefficient models. 1999. Vol. 27. In The annals of Statistics. pp.1491-1518. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113231418926814.
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