Adaptive varyingcoefficient linear models

Jianqing Fan Qiwei Yao Zongwu Cai

Statistics Theory and Methods mathscidoc:1912.43276

Journal of the Royal Statistical Society: series B (statistical methodology), 65, (1), 57-80, 2003.2
Varyingcoefficient linear models arise from multivariate nonparametric regression, nonlinear 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 <i>index</i>. To enlarge the modelling capacity substantially, this paper explores a class of varyingcoefficient 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 varyingcoefficient 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 onestep scheme
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  title={Adaptive varyingcoefficient linear models},
  author={Jianqing Fan, Qiwei Yao, and Zongwu Cai},
  booktitle={Journal of the Royal Statistical Society: series B (statistical methodology)},
Jianqing Fan, Qiwei Yao, and Zongwu Cai. Adaptive varyingcoefficient linear models. 2003. Vol. 65. In Journal of the Royal Statistical Society: series B (statistical methodology). pp.57-80.
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