Abstract
Variance estimation is a fundamental problem in statistical modelling and plays an important role in the inferences after model selection and estimation. In this paper, we focus on several nonparametric and semiparametric models and propose a local averaging method for variance estimation based on the concept of partial consistency. The proposed method has the advantages of avoiding the estimation of the nonparametric function and reducing the computational cost and can be easily extended to more complex settings. Asymptotic normality is established for the proposed local averaging estimators. Numerical simulations and a real data analysis are presented to illustrate the finite sample performance of the proposed method.
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Acknowledgements
The authors would like to thank the Editor, associate editor, and anonymous referees for their helpful comments and suggestions that have helped us to substantially improve the quality of the paper.
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Tao Huang’s research was supported in part by the State Key Program in the Major Research Plan of NSFC (No. 91546202), NSFC (No. 11771268) and Program for Innovative Research Team of SHUFE. Heng Peng’s research was supported part by CEGR Grant of the Research Grant Council of Hong Kong (Nos. HKBU202012 and HKBU12302615), FRG grant from the Hong Kong Baptist University (Nos. FRG214-15/064 and FRG2/16-17/042).
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Zhao, J., Peng, H. & Huang, T. Variance estimation for semiparametric regression models by local averaging. TEST 27, 453–476 (2018). https://doi.org/10.1007/s11749-017-0553-3
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DOI: https://doi.org/10.1007/s11749-017-0553-3