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Variance Reduction in Smoothing Splines

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  • ROBERT L. PAIGE
  • SHAN SUN
  • KEYI WANG

Abstract

. We develop a variance reduction method for smoothing splines. For a given point of estimation, we define a variance‐reduced spline estimate as a linear combination of classical spline estimates at three nearby points. We first develop a variance reduction method for spline estimators in univariate regression models. We then develop an analogous variance reduction method for spline estimators in clustered/longitudinal models. Simulation studies are performed which demonstrate the efficacy of our variance reduction methods in finite sample settings. Finally, a real data analysis with the motorcycle data set is performed. Here we consider variance estimation and generate 95% pointwise confidence intervals for the unknown regression function.

Suggested Citation

  • Robert L. Paige & Shan Sun & Keyi Wang, 2009. "Variance Reduction in Smoothing Splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 112-126, March.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:1:p:112-126
    DOI: 10.1111/j.1467-9469.2008.00616.x
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    References listed on IDEAS

    as
    1. Xihong Lin, 2004. "Equivalent kernels of smoothing splines in nonparametric regression for clustered/longitudinal data," Biometrika, Biometrika Trust, vol. 91(1), pages 177-193, March.
    2. Naisyin Wang, 2003. "Marginal nonparametric kernel regression accounting for within-subject correlation," Biometrika, Biometrika Trust, vol. 90(1), pages 43-52, March.
    3. Cheng, Ming-Yen & Hall, Peter, 2003. "Reducing variance in nonparametric surface estimation," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 375-397, August.
    4. X. Lin & D. Zhang, 1999. "Inference in generalized additive mixed modelsby using smoothing splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 381-400, April.
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