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January, 1994 On the Average Difference Between Concomitants and Order Statistics
Prem K. Goel, Peter Hall
Ann. Probab. 22(1): 126-144 (January, 1994). DOI: 10.1214/aop/1176988851


For a sequence of bivariate pairs $(X_i, Y_i)$, the concomitant $Y_{\lbrack i\rbrack}$ of the $i$th largest $x$-value $X_{(i)}$ equals that value of $Y$ paired with $X_{(i)}$. In assessing the quality of a file-merging or file-matching procedure, the penalty for incorrect matching may often be expressed as the average value of a function of the difference $Y_{\lbrack i\rbrack} - Y_{(i)}$. We establish strong laws and central limit theorems for such quantities. Our proof is based on the observation that if $G_x(\cdot)$ denotes the distribution function of $Y$ given $X = x$, then $G_X(Y)$ is stochastically independent of $X$, even though $G_x(\cdot)$ depends numerically on $x$.


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Prem K. Goel. Peter Hall. "On the Average Difference Between Concomitants and Order Statistics." Ann. Probab. 22 (1) 126 - 144, January, 1994.


Published: January, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0793.60019
MathSciNet: MR1258869
Digital Object Identifier: 10.1214/aop/1176988851

Primary: 60F05
Secondary: 60F15 , 62G30

Keywords: Bivariate order statistics , central limit theorem , concomitants , file-matching , file-merging , induced order statistics , Strong law of large numbers

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.22 • No. 1 • January, 1994
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