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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

   

 

An estimator of the location parameter obtained from observations with admixture


Author: O. Sugakova
Translated by: N. N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 80 (2009).
Journal: Theor. Probability and Math. Statist. 80 (2010), 143-152
MSC (2000): Primary 62G07; Secondary 62G20
Published electronically: August 20, 2010
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Abstract: We consider a model of observations from a two-component mixture such that the distribution of the admixture is known, while the distribution of the other component (treated as the primary one) is unknown. We assume that the distribution of the primary component is symmetric about the location parameter. We propose a method for constructing an unbiased estimating equation for the location parameter of the primary component. The asymptotic normality of the corresponding estimators is proved. The exact lower bound for the asymptotic variance is found and estimating functions for which this bound is attained are described. It is shown that the exact lower bound for the estimators under consideration is close to the corresponding bound of effectiveness of parametric estimators for the case where the distributions of both components are Gaussian.


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Additional Information

O. Sugakova
Affiliation: Department of Higher Mathematics and Theoretical Radiophysics, Faculty for Radiophysics, National Taras Shevchenko University, Academician Glushkov Avenue, 2, Kiev 03127, Ukraine
Email: sugak@univ.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-2010-00801-5
Keywords: Method of moments, a finite mixture of probability distributions, consistency, asymptotic normality, asymptotic variance
Received by editor(s): February 25, 2008
Published electronically: August 20, 2010
Article copyright: © Copyright 2010 American Mathematical Society