Wavelet block thresholding for density estimation in the presence of bias

We consider the density estimation problem from i.i.d, biased observations. The bias function is assumed to be bounded from above and below. A new adaptive estimator based on wavelet block thresholding is constructed. We evaluate these theoretical performances via the minimax approach under the L-P risk with p >= 1 (not only for p = 2) over a wide range of function classes: the Besov classes, B-pi,r(s) (with no particular restriction on the parameters pi and r). Under this general framework, we prove that it attains near optimal rates of convergence. The theory is illustrated by a numerical example. (C) 2009 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.