Title: How many point masses do we need for non-parametric deconvolution and maximum likelihood mixture densities?
Authors: Timothy Hyndman - The University of Melbourne (Australia) [presenting]
Peter Taylor - The University of Melbourne (Australia)
Aurore Delaigle - University of Melbourne (Australia)
Abstract: In non-parametric density deconvolution problems where the error distribution is unknown, one must solve an optimization problem to find a discrete probability distribution that approximates a continuous target distribution. In practice, this discrete distribution has surprisingly few point masses. The same phenomenon can also be observed when finding maximum likelihood mixture densities. The goal is to try to understand why this is happening, and to be able to say something about the number of point masses that will be required prior to performing the optimization. Some basic results for the maximum likelihood mixture problem will be presented by viewing the problem as an optimization problem, rather than a statistical one.