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

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