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Estimation of the parameters of the binomial distribution in a model of mixture


Author: A. Shcherbina
Translated by: S. V. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 86 (2012).
Journal: Theor. Probability and Math. Statist. 86 (2013), 205-217
MSC (2010): Primary 62F10; Secondary 62P10
DOI: https://doi.org/10.1090/S0094-9000-2013-00899-0
Published electronically: August 20, 2013
MathSciNet review: 2986460
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Abstract | References | Similar Articles | Additional Information

Abstract: A model for observations sampled from a two component mixture is considered. Each object is associated with a certain numerical characteristic that may assume two values, namely zero (failure) or one (success) with identical probabilities for all objects in every class. Probabilities for these values are constant for all objects from the same component. The total numbers of objects of the first and second classes in groups as well as their characteristics are known. We study the problem of estimation of success probabilities for both components. We solve the problem by using the maximum likelihood method. We prove that the estimator is consistent and asymptotically normal. We apply the results obtained in the paper to a problem in genetics. An explicit form of the estimator and the asymptotic dispersion matrix is presented.


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Additional Information

A. Shcherbina
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 4E, Kiev 03127, Ukraine
Email: artshcherbina@gmail.com

DOI: https://doi.org/10.1090/S0094-9000-2013-00899-0
Keywords: Estimation in a model of mixture, parametric estimation, genetic studies
Received by editor(s): May 20, 2011
Published electronically: August 20, 2013
Article copyright: © Copyright 2013 American Mathematical Society