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

DOI:
https://doi.org/10.1090/S0094-9000-2010-00801-5

Published electronically:
August 20, 2010

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://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