Activity Number:

641
 Recent Advances in Density Mixture Modeling and EMLike Algorithms: Frequentist and Bayesian Views

Type:

Topic Contributed

Date/Time:

Thursday, August 1, 2019 : 10:30 AM to 12:20 PM

Sponsor:

Section on Nonparametric Statistics

Abstract #305277

Presentation

Title:

A Regularization Based Approach to Estimation of a Two Component Nonparametric Density Mixture with a Known Component

Author(s):

Michael Levine* and Zuofeng Shang and Zhou Shen

Companies:

Purdue University and IUPUI and J.P. Morgan

Keywords:

penalized smoothed likelihood;
MM algorithm;
regularization

Abstract:

We consider a semiparametric mixture of two density functions where only one of them is known. Such mixtures have a history of application to the problem of detecting differentially expressed genes under two or more conditions in microarray data. We do not assume any additional structure on the unknown density function (e.g. symmetry). For this mixture model, we derive a new sufficient identifiability condition. We also suggest a novel approach to estimation of this model that is based on an idea of applying a maximum smoothed likelihood to what would otherwise have been an illposed problem. We introduce an iterative MM (MajorizationMinimization) algorithm that estimates all of the model parameters. We establish that the algorithm possesses a descent property with respect to a loglikelihood type objective functional and prove that the algorithm, indeed, converges. We also show how to establish the largesample convergence of the solution that the MM algorithm arrives at. Finally, we also illustrate the performance of our algorithm in a simulation study and using a real dataset. This is a joint work with Zuofeng Shang (IUPUI) and Zhou Shen (J.P. Morgan)
