Discrete probability density estimation using multirate DSP models

Abstract

We propose a model based approach for estimation of probability mass functions for discrete random variables. The model is based on tools from multirate signal processing. Similar in principle to the kernel based methods, the approach takes advantage of well-known results from multirate signal processing theory. Similarities to and differences from wavelet based approaches are also indicated where appropriate. In the final form, the probability estimates are obtained by filtering the square root of the histogram through a multirate system whose components are biorthogonal partners of each other.