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Efficient error variance estimation in non‐parametric regression

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  • Zhijian Li
  • Wei Lin

Abstract

Error variance estimation plays a key role in the analysis of homogeneous non‐parametric regression models. For a random design model, most methods in the literature for error variance estimation assume the independence between the predictor variable X and the error ε. In this work, we derive the optimal semi‐parametric efficiency bound for the error variance σ2=var(ϵ) without such an independence assumption. A residual‐based efficient estimator for σ2 is proposed and its asymptotic normality is established. An extensive simulation study is conducted, which shows that our proposed estimator works very favourably against competitors. A simple real‐data example is also presented.

Suggested Citation

  • Zhijian Li & Wei Lin, 2020. "Efficient error variance estimation in non‐parametric regression," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 62(4), pages 467-484, December.
    • Handle: RePEc:bla:anzsta:v:62:y:2020:i:4:p:467-484
    DOI: 10.1111/anzs.12311
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    References listed on IDEAS

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    5. WenWu Wang & Lu Lin & Li Yu, 2017. "Optimal variance estimation based on lagged second-order difference in nonparametric regression," Computational Statistics, Springer, vol. 32(3), pages 1047-1063, September.
    6. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    7. Wang, WenWu & Yu, Ping, 2017. "Asymptotically optimal differenced estimators of error variance in nonparametric regression," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 125-143.
    8. Jichang Du & Anton Schick, 2009. "A covariate-matched estimator of the error variance in nonparametric regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(3), pages 263-285.
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