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Theory of Probability and Mathematical Statistics

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Estimation of the mean value in a model of mixtures with varying concentrations

Author: A. Shcherbina
Translated by: S. V. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 84 (2011).
Journal: Theor. Probability and Math. Statist. 84 (2012), 151-164
MSC (2010): Primary 62G05; Secondary 62D05
Published electronically: August 2, 2012
MathSciNet review: 2857425
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a model for observations sampled from a two-component mixture. A certain numerical characteristic corresponds to every object. The distribution of the characteristic is unknown. The observations are obtained by sampling objects belonging to several groups. This procedure results in dependences among characteristics of objects, which constitute the difference between this setting and the classical one. The total amount of objects of the first and second class in each group is known, while the classes of objects are unknown. We consider the problem of estimation of mean values for characteristics of objects in each class. Two different settings are considered and expressions for the mean square errors are obtained for each of the settings. We show that the corresponding estimators are consistent and asymptotically normal.

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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 2, Kiev 03127, Ukraine

Keywords: Estimation in a model of mixtures, sampling method, nonparametric estimation
Received by editor(s): June 8, 2010
Published electronically: August 2, 2012
Article copyright: © Copyright 2012 American Mathematical Society

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