We formulate nonparametric density estimation as a constrained maximum likelihood problem whose constraints model any prior information available about the density. This technique will be used as a vehicle to illustrate the importance of including non-data information in the formulation of an estimation problem. For example, this non-data information may take the form of bounds on moments or specification of support, shape or smoothness. We will discuss theoretical questions about consistency and rate of convergence as well as address the practical issues of how to discretize and solve these problems numerically. Results of numerical experiments for some classical densities will be presented.
(This work is joint with Professor Roger Wets of UC Davis.)