Bias in Estimation of a Mixture of Normal Distributions
- *Corresponding Author:
- Jane S Paulsen
Departments of Psychiatry
Neurology and Psychology
University of Iowa, Iowa City
IA, 52442, USA
Tel: 319- 353-4551
Fax: (319) 353-3003
E-mail: [email protected]
Received Date: October 04, 2013; Accepted Date: November 19, 2013; Published Date: November 23, 2013
Citation: Lourens S, Zhang Y, Long JD, Paulsen JS (2013) Bias in Estimation of a Mixture of Normal Distributions. J Biomet Biostat 4:179. doi: 10.4172/2155-6180.1000179
Copyright: © 2013 Lourens S, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Estimating parameters in a mixture of normal distributions dates back to the 19th century when Pearson originally considered data of crabs from the Bay of Naples. Since then, many real world applications of mixtures have led to various proposed methods for studying similar problems. Among them, maximum likelihood estimation (MLE) and the continuous empirical characteristic function (CECF) methods have drawn the most attention. However, the performance of these competing estimation methods has not been thoroughly studied in the literature and conclusions have not been consistent in published research. In this article, we review this classical problem with a focus on estimation bias. An extensive simulation study is conducted to compare the estimation bias between the MLE and CECF methods over a wide range of disparity values. We use the overlapping coefficient (OVL) to measure the amount of disparity, and provide a practical guideline for estimation quality in mixtures of normal distributions. Application to an ongoing multi-site Huntington disease study is illustrated for ascertaining cognitive biomarkers of disease progression.