Global Measure of the Deviation of a Wavelet Density Estimator

Abstract

A wavelet estimator f*(x) of an unknown probability density function f(x)∈L2(R) is considered. A conditional central limit theorem for martingales is used to show that ∫([f *(x) − f (x)]^2)dx is asymptotically normally distributed. Results obtained can be used in a test of goodness-of-fit.