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September, 1973 Maximum Likelihood Estimation of a Translation Parameter of a Truncated Distribution
L. Weiss, J. Wolfowitz
Ann. Statist. 1(5): 944-947 (September, 1973). DOI: 10.1214/aos/1176342515

Abstract

$f(x)$ is a uniformly continuous density which equals zero for negative values of $x$, has a right-hand derivative equal to $\alpha$ at $x = 0$, where $0 < \alpha < \infty$, and satisfies certain regularity conditions. $X_1,\cdots, X_n$ are independent random variables with the common density $f(x - \theta), \theta$ an unknown parameter. Let $\hat{\theta}_n$ denote the maximum likelihood estimator of $\theta$, and define $\alpha_n$ by the equation $2\alpha_n^2 = \alpha n \log n$. It was shown by Woodroofe that the asymptotic distribution of $\alpha_n(\hat{\theta}_n - \theta)$ is standard normal. It is shown in the present paper that $\hat{\theta}_n$ is an asymptotically efficient estimator of $\theta$.

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L. Weiss. J. Wolfowitz. "Maximum Likelihood Estimation of a Translation Parameter of a Truncated Distribution." Ann. Statist. 1 (5) 944 - 947, September, 1973. https://doi.org/10.1214/aos/1176342515

Information

Published: September, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0271.62043
MathSciNet: MR341727
Digital Object Identifier: 10.1214/aos/1176342515

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 5 • September, 1973
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