An estimator of the location parameter obtained from observations with admixture

Sugakova, O.

doi:10.1090/S0094-9000-2010-00801-5

An estimator of the location parameter obtained from observations with admixture

Author: O. Sugakova
Translated by: N. N. Semenov
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
MathSciNet review: 2541959
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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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