Conditional density estimation based on hard threshold method

In this paper, we study the asymptotic behavior of the wavelet conditionaldensity function estimator under a new shrinkage method. The convergence rates forthe non-linear wavelet estimator are investigated. We evaluate these theoretical performancesvia the minimax approach under the Lp risk with p ۱ over a wide rangeof function classes: the Besov classes. Under mild assumptions on the model, we showthat it enjoys powerful mean integrated squared error properties. A simulation studyillustrates the good practical performance of our estimator.

Keywords:

Besov space , Hard threshold estimator , Conditional density , Nonparametricestimation , Wavelet methods