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Uniform asymptotics for kernel density estimators with variable bandwidths

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  • Evarist Giné
  • Hailin Sang

Abstract

It is shown that the Hall, Hu and Marron [Hall, P., Hu, T., and Marron J.S. (1995), ‘Improved Variable Window Kernel Estimates of Probability Densities’, Annals of Statistics, 23, 1–10] modification of Abramson's [Abramson, I. (1982), ‘On Bandwidth Variation in Kernel Estimates – A Square-root Law’, Annals of Statistics, 10, 1217–1223] variable bandwidth kernel density estimator satisfies the optimal asymptotic properties for estimating densities with four uniformly continuous derivatives, uniformly on bounded sets where the preliminary estimator of the density is bounded away from zero.

Suggested Citation

  • Evarist Giné & Hailin Sang, 2010. "Uniform asymptotics for kernel density estimators with variable bandwidths," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(6), pages 773-795.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:6:p:773-795
    DOI: 10.1080/10485250903483331
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    Cited by:

    1. David Mason, 2012. "Proving consistency of non-standard kernel estimators," Statistical Inference for Stochastic Processes, Springer, vol. 15(2), pages 151-176, July.
    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.
    3. Yunan Wu & Lan Wang, 2021. "Resampling‐based confidence intervals for model‐free robust inference on optimal treatment regimes," Biometrics, The International Biometric Society, vol. 77(2), pages 465-476, June.

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