Mixtures of Normal Distributions, Revisited

• Activity Number: 687
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Spencer Lourens*+ and Ying J. Zhang
• Companies: University of Iowa, College of Public Health and University of Iowa
• Keywords: AUC ; Mixture ; EM algorithm

Abstract

Estimation of parameters for mixtures of normal distributions has been considered since the 19th century when Pearson originally considered data consisting of ratios of forehead to body length of crabs from the Bay of Naples. We revisit the mixture of normal distributions in the small sample, poor-separation case previously considered by Hosmer (1973) and Leytham (1984) and develop a Standardized AUC index that can be used to assess separation between the two normal distributions. It will be shown that estimates from the EM algorithm can be biased and imprecise in these cases, and comparisons between EM estimates and estimates minimizing a squared error loss function (Continuous Empirical Charateristic Function Method, CECF) will be made. We hope to discuss inherent bias in estimating the AUC when the method of estimation is itself, biased.