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Variance estimation for semiparametric regression models by local averaging

Author

Listed:
  • Jingxin Zhao

    (Hong Kong Baptist University)

  • Heng Peng

    (Hong Kong Baptist University)

  • Tao Huang

    (Shanghai University of Finance and Economics)

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.

Suggested Citation

  • Jingxin Zhao & Heng Peng & Tao Huang, 2018. "Variance estimation for semiparametric regression models by local averaging," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 453-476, June.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:2:d:10.1007_s11749-017-0553-3
    DOI: 10.1007/s11749-017-0553-3
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    References listed on IDEAS

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    1. Jianqing Fan & Shaojun Guo & Ning Hao, 2012. "Variance estimation using refitted cross‐validation in ultrahigh dimensional regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(1), pages 37-65, January.
    2. Cai, T. Tony & Levine, Michael & Wang, Lie, 2009. "Variance function estimation in multivariate nonparametric regression with fixed design," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 126-136, January.
    3. Tiejun Tong & Yuedong Wang, 2005. "Estimating residual variance in nonparametric regression using least squares," Biometrika, Biometrika Trust, vol. 92(4), pages 821-830, December.
    4. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
    5. Fan, Jianqing & Peng, Heng & Huang, Tao, 2005. "Semilinear High-Dimensional Model for Normalization of Microarray Data: A Theoretical Analysis and Partial Consistency," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 781-796, September.
    6. Zhang, Wenyang & Lee, Sik-Yum, 2000. "Variable Bandwidth Selection in Varying-Coefficient Models," Journal of Multivariate Analysis, Elsevier, vol. 74(1), pages 116-134, July.
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    Cited by:

    1. Peng, Heng & Xie, Chuanlong & Zhao, Jingxin, 2021. "Fast inference for semi-varying coefficient models via local averaging," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).

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