# Nonparametric Curve Estimation by Smoothing Splines: Unbiased-Risk-Estimate Selector and its Robust Version via Randomized Choices

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This Demonstration considers a simple nonparametric regression problem: how to recover a function of one variable, here over , when only couples () are known for that satisfy the model , where and the are independent, standard normal random variables. For simplicity, assume that the variance is also known.

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Contributed by: Didier A. Girard (September 2017)

(CNRS-LJK and Univ. Grenoble Alpes)

Open content licensed under CC BY-NC-SA

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References

[1] D. A. Girard, "Nonparametric Curve Estimation by Kernel Smoothers: Efficiency of Unbiased Risk Estimate and GCV Selectors," from the Wolfram Demonstrations Project—A Wolfram Web Resource. (Jan 9, 2013) demonstrations.wolfram.com/NonparametricCurveEstimationByKernelSmoothersEfficiencyOfUnb.

[2] jojosthegreat, "Implementation of Smoothing Splines Function," Mathematica Stack Exchange. (Sep 5, 2017) mathematica.stackexchange.com/questions/33206/implementation-of-smoothing-splines-function/33262.

[3] M. A. Lukas, F. R. de Hoog and R. S. Anderssen, "Practical Use of Robust GCV and Modified GCV for Spline Smoothing," C*omputational Statistics*, 31(1), 2016 pp. 269–289. do:10.1007/s00180-015-0577-7.

[4] D. A. Girard, "Estimating the Accuracy of (Local) Cross-Validation via Randomised GCV Choices in Kernel or Smoothing Spline Regression," *Journal of Nonparametric Statistics*, 22(1), 2010 pp. 41–64. doi:10.1080/10485250903095820.

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