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Pointwise Sharp Moderate Deviations for a Kernel Density Estimator

Author

Listed:
  • Siyu Liu

    (School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

  • Xiequan Fan

    (School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

  • Haijuan Hu

    (School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

  • Paul Doukhan

    (CY University, AGM UMR 8088, Saint-Martin, 95000 Cergy-Pontoise, France)

Abstract

Let f n be the non-parametric kernel density estimator based on a kernel function K and a sequence of independent and identically distributed random vectors taking values in R d . With some mild conditions, we establish sharp moderate deviations for the kernel density estimator. This means that we provide an equivalent for the tail probabilities of this estimator.

Suggested Citation

  • Siyu Liu & Xiequan Fan & Haijuan Hu & Paul Doukhan, 2024. "Pointwise Sharp Moderate Deviations for a Kernel Density Estimator," Mathematics, MDPI, vol. 12(20), pages 1-9, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3161-:d:1495186
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    References listed on IDEAS

    as
    1. Fuqing Gao, 2003. "Moderate Deviations and Large Deviations for Kernel Density Estimators," Journal of Theoretical Probability, Springer, vol. 16(2), pages 401-418, April.
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