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The American Statistician Volume 60, 2006 - Issue 1
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Primary Article

MVUE for the Mean With One Observation

Normal with Same Mean and Variance

Nitis Mukhopadhyay Nitis Mukhopadhyay is Professor, Department of Statistics, UBox 4120, University of Connecticut, Storrs, CT 06269-4120 . I thank both the editor, James H. Albert, and a referee for many helpful remarks. I remain especially indebted to Professor Albert for a series of editorial pointers. I also thank my colleague, Enrique Alvarez, for commenting on a preliminary version.
Pages 71-74 | Published online: 01 Jan 2012
 
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Abstract

Based on one observation X from a N(θ, θ) distribution where θ(> 0) is an unknown parameter, this article provides an exact expression of the minimum variance unbiased estimator of θ based on the complete and sufficient statistic ||X||. Even though N(θ, θ)belongs to a one-parameter exponential family, I discuss some small surprises and intricacies that are worth noting.

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