Some new methods for wavelet density estimation

David R.M. Herrick, Guy P. Nason and Bernard W. Silverman

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 coefficients. One proposed method of estimating the variances of the raw coefficients uses the scaling function coefficients. Since these are available as a by-product of the discrete wavelet transform, no extra effort is required to find 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.