Some New Methods for Wavelet Density Estimation

This article proposes some non-linear, thresholded wavelet density estimators, and investigates the practical problems involved in their implementation. Our proposed thresholding method exploits the non-stationary variance structure of the wavelet coe cients. One proposed method of estimating the variances of the raw coe cients uses the scaling function coe cients. Since these are available as a by-product of the discrete wavelet transform, no extra e ort is required to nd them. The performance of the methodology is assessed on a real dataset from a forensic application and simulated data from a well known test function.