Estimating Component Cumulative Distribution Functions in Finite Mixture Models

• Published in: Communications in statistics. Theory and methods Vol. 33; no. 9; pp. 2075 - 2086
• Main Authors: Elmore, Ryan T., Hettmansperger, Thomas P., Thomas, Hoben
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 31.12.2004; Taylor & Francis
• Subjects: Applications; Biology, psychology, social sciences; Cut-point model; Distribution theory; Empirical distribution function; Exact sciences and technology; Mathematics; Moment estimation; Multinomial mixture; Primary 62; Probability and statistics; Sciences and techniques of general use; Secondary 62G, 62G99; Statistics; Mixed distribution; Statistical method; Distribution function; Estimating function; Multinomial distribution; Cognitive psychology
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1081/STA-200026574

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.