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2 results

  • Adaptive estimation of a density function using beta kernels

  • Karine Bertin, Nicolas Klutchnikoff
  • Journal:
    ESAIM: Probability and Statistics / Volume 18 / 2014
    Published online by Cambridge University Press:
    08 October 2014, pp. 400-417
    Print publication:
    2014

  • In this paper we are interested in the estimation of a density − defined on a compact interval ofℝ− from n independent andidentically distributed observations. In order to avoid boundary effect, beta kernelestimators are used and we propose a procedure (inspired by Lepski’s method) in order toselect the bandwidth. Our procedure is proved to be adaptive in an asymptotically minimaxframework. Our estimator is compared with both the cross-validation algorithm and theoracle estimator using simulated data.