Bias reduction for nonparametric and semiparametric regression models

Ming-Yen CHENG, Tao Huang, Peng Liu, Heng PENG

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)2749-2770
Number of pages22
JournalStatistica Sinica
Volume28
Issue number4
DOIs
Publication statusPublished - Oct 2018

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Simultaneous confidence band
  • Undersmoothing
  • Variance function estimation

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