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Estimating residual variance in nonparametric regression using least squares

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  • Tiejun Tong
  • Yuedong Wang
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    Abstract

    We propose a new estimator for the error variance in a nonparametric regression model. We estimate the error variance as the intercept in a simple linear regression model with squared differences of paired observations as the dependent variable and squared distances between the paired covariates as the regressor. For the special case of a one-dimensional domain with equally spaced design points, we show that our method reaches an asymptotic optimal rate which is not achieved by some existing methods. We conduct extensive simulations to evaluate finite-sample performance of our method and compare it with existing methods. Our method can be extended to nonparametric regression models with multivariate functions defined on arbitrary subsets of normed spaces, possibly observed on unequally spaced or clustered designed points. Copyright 2005, Oxford University Press.

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    File URL: http://hdl.handle.net/10.1093/biomet/92.4.821
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    Bibliographic Info

    Article provided by Biometrika Trust in its journal Biometrika.

    Volume (Year): 92 (2005)
    Issue (Month): 4 (December)
    Pages: 821-830

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    Handle: RePEc:oup:biomet:v:92:y:2005:i:4:p:821-830

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    Postal: Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK
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    Cited by:
    1. Peter Hall & Joel Horowitz, 2013. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers CWP29/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Eckhard Liebscher, 2012. "Model checks for parametric regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 21(1), pages 132-155, March.
    3. Paul Hall & Joel Horowitz, 2012. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers CWP14/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. LiitiƤinen, Elia & Corona, Francesco & Lendasse, Amaury, 2010. "Residual variance estimation using a nearest neighbor statistic," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 811-823, April.
    5. Mendez, Guillermo & Lohr, Sharon, 2011. "Estimating residual variance in random forest regression," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2937-2950, November.

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