On the asymptotlc normality for l₂-error of wavelei density estimator with application

Abstract

The l₂ error of linear wavelet estimator of a density from a random sample is shown to be asymptotically normal without imposing smoothing conditions on the density. As an application, the goodness-of-fit test and the approximation of its power for closeness alternatives are considered.

Keywords:

• nonparametric density estimation
• central Imiit theorein
• wavelet