This article is cited in 2 papers

Short Communications

On estimation of a location parameter in presence of an ancillary component

A. M. Kagan^a, C. R. Rao<sup>b

a</sup> University of Maryland
^b Pennsylvania State University

Abstract: If $(X, Y)$ is an observation with distribution function $F(x-\theta,y)$, $\sigma^{2}=\textrm{var}(X)$, $\rho=\textrm{corr}(X,Y)$ and $I$ is the Fisher information on $\theta$ in $(X,Y)$, then $I\ge\{\sigma^2(1-\rho^2)\}^{-1}$. The equality sign holds under conditions closely related to the conditions for linearity of the Pitman estimator of $\theta$ from a sample from $F(x-\theta,y)$. The results are extensions of earlier results for the case when only the informative component $X$ is observed.

Keywords: Fisher information, Pitman estimator.

Received: 21.09.2004

Language: English

DOI: 10.4213/tvp166

 English version: Theory of Probability and its Applications, 2006, 50:1, 129–133

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