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.
|Number of pages||15|
|Journal||Communications in Statistics - Simulation and Computation|
|Early online date||4 Sep 2019|
|Publication status||Published - 2022|
- Quantile density function
- Lp risk function
- Block thresholding