Nonparametric estimation of a quantile density function under Lp risk via block thresholding method

Esmaeil Shirazi*, Hassan Doosti

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)

    Abstract

    Here we propose a new quantile density function estimator via block thresholding methods and investigate its asymptotic convergence rates under Lp risk with p≥2 over Besov balls. We show that the considered estimator achieves optimal or near optimal rates of convergence according to the values of the parameter ν of the Besov classes Bs v,q. We show that this estimator attain optimal and nearly optimal rates of convergence over a wide range of Besov function classes, and in particular enjoys those faster rates without the extraneous logarithmic penalties that given in Chesneau et al. A simulation study shows new proposed estimator performs better at the tails than existing competitors.

    Original languageEnglish
    Pages (from-to)539-553
    Number of pages15
    JournalCommunications in Statistics - Simulation and Computation
    Volume51
    Issue number2
    Early online date4 Sep 2019
    DOIs
    Publication statusPublished - 2022

    Keywords

    • Adaptivity
    • Quantile density function
    • Lp risk function
    • Wavelets
    • Block thresholding

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