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On local bootstrap bandwidth choice in kernel density estimation

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  • Ziegler Klaus

Abstract

Under mild regularity conditions, it is shown that bandwidth selection by minimizing the bootstrapped mean squared error (at a point x) leads to a bandwidth of the same form as that obtained by a consistent plug-in procedure. The consequences of this observation for the construction of confidence intervals are also discussed.

Suggested Citation

  • Ziegler Klaus, 2006. "On local bootstrap bandwidth choice in kernel density estimation," Statistics & Risk Modeling, De Gruyter, vol. 24(2), pages 1-11, December.
    • Handle: RePEc:bpj:strimo:v:24:y:2006:i:2:p:11:n:5
    DOI: 10.1524/stnd.2006.24.2.291
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    References listed on IDEAS

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    1. Stephan R. Sain & David W. Scott, 2002. "Zero‐Bias Locally Adaptive Density Estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 441-460, September.
    2. Abramson, Ian S., 1982. "Arbitrariness of the pilot estimator in adaptive kernel methods," Journal of Multivariate Analysis, Elsevier, vol. 12(4), pages 562-567, December.
    3. Joseph Romano, 1988. "Bootstrapping the mode," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(3), pages 565-586, September.
    4. 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. 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.
    2. 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.

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