On the L~p-Consistency of Wavelet Estimators

This paper deals with the L~p-consistency of wavelet estimators for a density function based on size-biased random samples. More precisely, we firstly show the L~p-consistency of wavelet estimators for independent and identically distributed random vectors in R~d. Then a similar result is obtained for negatively associated samples under the additional assumptions d = 1 and the monotonicity of the weight function.