Estimating Component Cumulative Distribution Functions in Finite Mixture Models

Abstract

We propose a method of estimating component distribution functions (cdfs) in finite mixture distributions without specifying a parametric form on the true underlying cdfs. As a result, we develop estimators of the component parameters based on these estimated cdfs. This method requires a vector of observations on each subject and involves discretizing the original data into multinomial bins. This results in a mixture of multinomial distributions which has the same mixing proportions as the original mixture. The methods are illustrated on a data set from cognitive psychology.

Key Words:

• Cut-point model
• Empirical distribution function
• Moment estimation
• Multinomial mixture

Mathematics Subject Classification:

• Primary 62
• Secondary 62G, 62G99

Acknowledgment

The research was partially supported by the National Science Foundation grant SES-0115619.