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

DOI:
https://doi.org/10.1090/S0094-9000-2012-00866-1

Published electronically:
August 2, 2012

MathSciNet review:
2857425

Full-text PDF Free Access

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

Email:
artshcherbina@gmail.com

DOI:
https://doi.org/10.1090/S0094-9000-2012-00866-1

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