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A Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric Regression

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  • Yuejin Zhou
  • Yebin Cheng
  • Tiejun Tong

Abstract

Interest in variance estimation in nonparametric regression has grown greatly in the past several decades. Among the existing methods, the least squares estimator in Tong and Wang (2005) is shown to have nice statistical properties and is also easy to implement. Nevertheless, their method only applies to regression models with homoscedastic errors. In this paper, we propose two least squares estimators for the error variance in heteroscedastic nonparametric regression: the intercept estimator and the slope estimator. Both estimators are shown to be consistent and their asymptotic properties are investigated. Finally, we demonstrate through simulation studies that the proposed estimators perform better than the existing competitor in various settings.

Suggested Citation

  • Yuejin Zhou & Yebin Cheng & Tiejun Tong, 2014. "A Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric Regression," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:585146
    DOI: 10.1155/2014/585146
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    References listed on IDEAS

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    1. H. Dette & A. Munk & T. Wagner, 1998. "Estimating the variance in nonparametric regression—what is a reasonable choice?," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 751-764.
    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. Hardle, W. & Tsybakov, A., 1997. "Local polynomial estimators of the volatility function in nonparametric autoregression," Journal of Econometrics, Elsevier, vol. 81(1), pages 223-242, November.
    4. 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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