Variable bandwidth and local linear regression smoothers

Jianqing Fan Irene Gijbels

Statistics Theory and Methods mathscidoc:1912.43253

The Annals of Statistics, 2008-2036, 1992.12
In this paper we introduce an appealing nonparametric method for estimating the mean regression function. The proposed method combines the ideas of local linear smoothers and variable bandwidth. Hence, it also inherits the advantages of both approaches. We give expressions for the conditional MSE and MISE of the estimator. Minimization of the MISE leads to an explicit formula for an optimal choice of the variable bandwidth. Moreover, the merits of considering a variable bandwidth are discussed. In addition, we show that the estimator does not have boundary effects, and hence does not require modifications at the boundary. The performance of a corresponding plug-in estimator is investigated. Simulations illustrate the proposed estimation method.
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  title={Variable bandwidth and local linear regression smoothers},
  author={Jianqing Fan, and Irene Gijbels},
  booktitle={The Annals of Statistics},
Jianqing Fan, and Irene Gijbels. Variable bandwidth and local linear regression smoothers. 1992. In The Annals of Statistics. pp.2008-2036.
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