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Bias Reduction for Nonparametric and Semiparametric Regression Models

Cheng, Ming-Yen, Huang, Tao, LIU, Peng, Peng, Heng (2018) Bias Reduction for Nonparametric and Semiparametric Regression Models. Statistica Sinica, 28 . pp. 2749-2770. ISSN 1017-0405. (doi:10.5705/ss.202017.0058) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided)

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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.

Item Type: Article
DOI/Identification number: 10.5705/ss.202017.0058
Uncontrolled keywords: Simultaneous confidence band, undersmoothing, variance function estimation.
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Peng Liu
Date Deposited: 09 Aug 2019 10:04 UTC
Last Modified: 20 Jan 2020 16:29 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/75735 (The current URI for this page, for reference purposes)
LIU, Peng: https://orcid.org/0000-0002-0492-0029
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