Multiwavelet density estimation for biased data

摘要

In this article, we present our method for multiwavelet estimation for a density function based on random samples from a weighted distribution. First, we propose linear and nonlinear multiwavelet estimators for the biased data. Then, we provide and prove the upper bound of Lp risk for the proposed nonlinear estimator over a large class of densities in the Besov space, Br1,qs. Finally, we provide simulation and real data experiments to illustrate the effectiveness and behavior of the proposed method and estimator.