Nonparametric density estimation using wavelet transformation and scale-space zero-crossing reconstruction

Parzen window method requires relatively larger sample set, and the result of estimation is subject to the selection of window width, so the Parzen window method cannot get good estimation to complex distribution that needs multi-resolution. A novel approach, which is based upon wavelet transformation is presented. On the viewpoint of wavelet transformation, the result of Parzen window method is only the smoothing approximation of p.d.f.. Scale space filter technology is used to get rid of the noise produced by smaller sample set. Six simulations show out that this method can successfully solve the dilemma of estimating of p.d.f. by small sample set and complex distribution.