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Variance estimation in nonparametric regression with jump discontinuities

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  • Wenlin Dai
  • Tiejun Tong

Abstract

Variance estimation is an important topic in nonparametric regression. In this paper, we propose a pairwise regression method for estimating the residual variance. Specifically, we regress the squared difference between observations on the squared distance between design points, and then estimate the residual variance as the intercept. Unlike most existing difference-based estimators that require a smooth regression function, our method applies to regression models with jump discontinuities. Our method also applies to the situations where the design points are unequally spaced. Finally, we conduct extensive simulation studies to evaluate the finite-sample performance of the proposed method and compare it with some existing competitors.

Suggested Citation

  • Wenlin Dai & Tiejun Tong, 2014. "Variance estimation in nonparametric regression with jump discontinuities," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(3), pages 530-545, March.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:3:p:530-545
    DOI: 10.1080/02664763.2013.842962
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    References listed on IDEAS

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    1. Sim, C.H. & Gan, F.F. & Chang, T.C., 2005. "Outlier Labeling With Boxplot Procedures," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 642-652, June.
    2. Tiejun Tong & Yuedong Wang, 2005. "Estimating residual variance in nonparametric regression using least squares," Biometrika, Biometrika Trust, vol. 92(4), pages 821-830, December.
    3. 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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    Cited by:

    1. 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.
    2. Ieva Axt & Roland Fried, 2020. "On variance estimation under shifts in the mean," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 417-457, September.

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