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March, 1980 Estimation of the Correlation Coefficient from a Broken Random Sample
Morris H. DeGroot, Prem K. Goel
Ann. Statist. 8(2): 264-278 (March, 1980). DOI: 10.1214/aos/1176344952


Inference about the correlation coefficient $\rho$ in a bivariate normal distribution is considered when observations from the distribution are available only in the form of a broken random sample. In other words, a random sample of $n$ pairs is drawn from the distribution but the observed data are only the first components of the $n$ pairs and, separately, some unknown permutation of the second components of the $n$ pairs. Under these conditions, the estimation of $\rho$ is, as Samuel Johnson put it, "like a dog's walking on his hinder legs. It is not done well; but you are surprised to find it done at all." We study the maximum likelihood estimation of $\rho$ and present some effective procedures for estimating the sign of $\rho$.


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Morris H. DeGroot. Prem K. Goel. "Estimation of the Correlation Coefficient from a Broken Random Sample." Ann. Statist. 8 (2) 264 - 278, March, 1980.


Published: March, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0446.62049
MathSciNet: MR560728
Digital Object Identifier: 10.1214/aos/1176344952

Primary: 62F10
Secondary: 62C99, 62H20

Rights: Copyright © 1980 Institute of Mathematical Statistics


Vol.8 • No. 2 • March, 1980
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