Esmaeil Shirazi - Department of Statistics, Faculty of Science, Gonbad Kavous University, Gonbad Kavous, Iran.
Abdolsaeed Toomaj - Department of Statistics, Faculty of Science, Gonbad Kavous University, Gonbad Kavous, Iran.

Here we consider wavelet-based identification and estimation of a quantile density function via block thresholding methods and investigate their asymptotic convergence rates. We show that these estimators, based on block thresholding of empirical wavelet coefficients, achieve optimal convergence rates over a large range of Besov function classes, and in particular enjoy those rates without the extraneous logarithmic penalties that are usually suffered by term-by-term thresholding methods.

block thresholding method, Quantile density estimation, Wavelets