Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

Nonparametric and semiparametric regression models are useful statistical regression models to discover nonlinear relationships between the response variable and predictor variables. However, optimal efficient estimators for the nonparametric components in the models are biased which hinders the development of methods for further statistical inference. In this paper, based on the local linear fitting, we propose a simple bias reduction approach for the estimation of the nonparametric regression model. Our approach does not need to use higher-order local polynomial regression to estimate the bias, and hence avoids the double bandwidth selection and design sparsity problems suffered by higher-order local polynomial fitting. It also does not inflate the variance. Hence it can be easily applied to complex statistical inference problems. We extend our approach to varying coefficient models, to estimate the variance function, and to construct simultaneous confidence band for the nonparametric regression function. Simulations are carried out for comparisons with existing methods, and a data example is used to investigate the performance of the proposed method.

Keywords

Simultaneous confidence band, undersmoothing, variance function estimation

Publication Date

10-2018

Source Publication Title

Statistica Sinica

Volume

28

Issue

4

Start Page

2749

End Page

2770

Publisher

Academia Sinica, Institute of Statistical Science

DOI

10.5705/ss.202017.0058

Link to Publisher's Edition

https://doi.org/10.5705/ss.202017.0058

ISSN (print)

10170405

ISSN (electronic)

19968507

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