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 journalArticle

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
Number of pages15
JournalCommunications in Statistics - Simulation and Computation
DOIs
Publication statusE-pub ahead of print - 4 Sep 2019

Keywords

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

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