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

Abstract

Here we propose a new quantile density function estimator via block thresholding methods and investigate its asymptotic convergence rates under L_p risk with $p\ge 2$ 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 $B_{\nu ,q}^s$. 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.

KEYWORDS:

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

MATHEMATICS SUBJECT CLASSIFICATION (2010):

• 62G07
• 62G20