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On nonparametric local inference for density estimation

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  • Chan, Ngai-Hang
  • Lee, Thomas C.M.
  • Peng, Liang

Abstract

Bandwidth selection has been an important topic in nonparametric density estimation. In this paper an effective method for local bandwidth selection is proposed. For local bandwidth selection, due to data sparsity and other reasons, extremely small bandwidths are sometimes selected, which lead to severe undersmoothing. To circumvent this difficulty, the main idea behind the proposed method is to choose the largest bandwidth that still achieves the optimal rate. When coupled with practical bias reduction techniques, the bandwidth selected from this method can be applied simultaneously to conduct both local point and interval estimation. Simulation studies demonstrate the effectiveness of the proposed approach, which compares favorably with other existing approaches.

Suggested Citation

  • Chan, Ngai-Hang & Lee, Thomas C.M. & Peng, Liang, 2010. "On nonparametric local inference for density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 509-515, February.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:2:p:509-515
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    References listed on IDEAS

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    1. Armelle Guillou & Peter Hall, 2001. "A diagnostic for selecting the threshold in extreme value analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 293-305.
    2. Sheather, Simon, 1983. "A data-based algorithm for choosing the window width when estimating the density at a point," Computational Statistics & Data Analysis, Elsevier, vol. 1(1), pages 229-238, March.
    3. Einmahl, John H. J., 1997. "Poisson and Gaussian approximation of weighted local empirical processes," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 31-58, October.
    4. Sheather, Simon J., 1986. "An improved data-based algorithm for choosing the window width when estimating the density at a point," Computational Statistics & Data Analysis, Elsevier, vol. 4(1), pages 61-65, June.
    5. Peter Hall & Michael C. Minnotte, 2002. "High order data sharpening for density estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 141-157, January.
    6. Ziegler Klaus, 2006. "On local bootstrap bandwidth choice in kernel density estimation," Statistics & Risk Modeling, De Gruyter, vol. 24(2), pages 1-11, December.
    7. Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February.
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    Cited by:

    1. Adriano Z. Zambom & Ronaldo Dias, 2013. "A Review of Kernel Density Estimation with Applications to Econometrics," International Econometric Review (IER), Econometric Research Association, vol. 5(1), pages 20-42, April.
    2. Golyandina, Nina & Pepelyshev, Andrey & Steland, Ansgar, 2012. "New approaches to nonparametric density estimation and selection of smoothing parameters," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2206-2218.

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