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March, 1975 Relationships Between the UMVU Estimators of the Mean and Median of a Function of a Normal Distribution
Farhad Mehran
Ann. Statist. 3(2): 457-460 (March, 1975). DOI: 10.1214/aos/1176343071

Abstract

Let $\eta = f(\mu)$ and $\theta = Ef(Y)$, where $f$ is a monotone function and $Y \sim N(\mu, \sigma^2)$. In this note we use the method of convolution transforms to show that the UMVU estimators of $\eta$ and $\theta$ based on a pair of independent sufficient statistics $T \sim N(\mu, \alpha \sigma^2)$ and $S^2 \sim \sigma^2 \chi^2_{(\nu)}$ are related to each other in a simple manner: the replacement $\alpha$ by $\alpha - 1$ in the expression of the UMVU estimator of $\eta$ gives the corresponding expression of the UMVU estimator of $\theta$. In addition, we show that a similar relationship also exists among the estimators of the variances.

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Farhad Mehran. "Relationships Between the UMVU Estimators of the Mean and Median of a Function of a Normal Distribution." Ann. Statist. 3 (2) 457 - 460, March, 1975. https://doi.org/10.1214/aos/1176343071

Information

Published: March, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0303.62025
MathSciNet: MR381106
Digital Object Identifier: 10.1214/aos/1176343071

Subjects:
Primary: 62B05
Secondary: 62F10 , 62J99

Keywords: function of normal distribution , UMVU estimation

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 2 • March, 1975
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