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 LpLp risk with p≥1p≥1 (not only for p=2p=2) over a wide range of function classes: the Besov classes, Bπ,rs (with no particular restriction on the parameters ππ and rr). Under this general framework, we prove that it attains near optimal rates of convergence. The theory is illustrated by a numerical example.