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 $x$.
Publié le : 1994-01-14
Classification:
Bivariate order statistics,
central limit theorem,
concomitants,
file-matching,
file-merging,
induced order statistics,
strong law of large numbers,
60F05,
60F15,
62G30
@article{1176988851,
author = {Goel, Prem K. and Hall, Peter},
title = {On the Average Difference Between Concomitants and Order Statistics},
journal = {Ann. Probab.},
volume = {22},
number = {4},
year = {1994},
pages = { 126-144},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988851}
}
Goel, Prem K.; Hall, Peter. On the Average Difference Between Concomitants and Order Statistics. Ann. Probab., Tome 22 (1994) no. 4, pp. 126-144. http://gdmltest.u-ga.fr/item/1176988851/