Seminar at SMU Delhi

Modeling mixture distributions is a well studied problem in statistics. In this talk we consider a special case where the data come from a mixture of an arbitrary decreasing density and a parametric density, a model that has applications in particle physics and astrophysics. As is common with mixture modeling, we use the EM algorithm to find maximum likelihood estimates, using a variant of Grenander's least concave majorant estimator to estimate the decreasing density. Simulation is used to explore the performance of our estimators, and challenges involved in establishing their asymptotic properties are discussed briefly. We also discuss modifications required in the case of binned data, which is common in applied settings, and has the advantage that the model reduces to a finite-dimensional one. This is joint work with Deepayan Sarkar.