Asymptotic normality of the multiscale wavelet density estimator

Abstract

A multiscale wavelet density estimator (MWDE) was recently introduced and was shown to have nice convergence properties as well as good simulation results (Wu, 1995). This paper studies the asymptotic normality of the MWDE. It is proved that, under mild conditions, the MWDE has the asymptotic normality in the support of the unknown density f.As by-products, the author establishes the asymptotic normality of the wavelet estimator and discovers several interesting statistical properties of the reproducing kernel q_m(x,t)ofV_m .

Keywords:

• subestimator
• reproducing kernel
• delta-sequence