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Reducing variance in nonparametric surface estimation

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  • Cheng, Ming-Yen
  • Hall, Peter

Abstract

We suggest a method for reducing variance in nonparametric surface estimation. The technique is applicable to a wide range of inferential problems, including both density estimation and regression, and to a wide variety of estimator types. It is based on estimating the contours of a surface by minimising deviations of elementary surface estimates along a quadratic curve. Once a contour estimate has been obtained, the final surface estimate is computed by averaging conventional surface estimates along a portion of the contour. Theoretical and numerical properties of the technique are discussed.

Suggested Citation

  • Cheng, Ming-Yen & Hall, Peter, 2003. "Reducing variance in nonparametric surface estimation," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 375-397, August.
    • Handle: RePEc:eee:jmvana:v:86:y:2003:i:2:p:375-397
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    References listed on IDEAS

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    1. H. G. Müller & U. Stadtmüller, 1999. "Multivariate boundary kernels and a continuous least squares principle," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 439-458, April.
    2. Hall, P. & Huber, C. & Owen, A. & Coventry, A., 1994. "Asymptotically Optimal Balloon Density Estimates," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 352-371, November.
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    Cited by:

    1. 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.

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