Continuous non-negative wavelets and their use in density estimation
Gilbert G. Walter, Xiaoping Shen · Communication in Statistics- Theory and Methods · 1999
It was shown by Janssen in 1993 that there are no continuous non-negative orthogonal scaling functions. For density estimation, we would like the estimators themselves to be densities, and hence non-negative. Thus the usual linear projection or the threshold estimators won't work without modification. In this paper, we introduce smooth non-negative wavelet estimators. The density estimators based on them are themselves density functions. These are applied to two numerical examples and compared to the usual wavelet estimators in these examples. An associated noise reduction method is considered.