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.
Alyass, Kussiy K.
"Global Measure of the Deviation of a Wavelet Density Estimator,"
Journal of Modern Applied Statistical Methods: Vol. 6
, Article 19.
Available at: http://digitalcommons.wayne.edu/jmasm/vol6/iss2/19