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- W2014798451 abstract "For a random sample of size $n$ from an absolutely continuous bivariate population $(X, Y)$, let $X_{i:n}$ denote the $i$th order statistic of the $X$ sample values. The $Y$-value associated with $X_{i:n}$ is denoted by $Y_{lbrack i:nrbrack}$ and is called the concomitant of the $i$th order statistic. For $1 leq k leq n$, let $V_{k,n} = max(Y_{lbrack n - k + 1: nrbrack},ldots,Y_{lbrack n: nrbrack})$. In this paper, we discuss the finite-sample and the asymptotic distributions of $V_{k,n}$. We investigate the limit distribution of $V_{k,n}$ as $n rightarrow infty$, when $k$ is held fixed and when $k = lbrack nprbrack, 0 < p < 1$. In both cases we obtain simple sufficient conditions and determine the associated norming constants. We apply our results to some interesting situations, including the bivariate normal population and the simple linear regression model." @default.
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- W2014798451 date "1994-03-01" @default.
- W2014798451 modified "2023-10-18" @default.
- W2014798451 title "Distribution of the Maximum of Concomitants of Selected Order Statistics" @default.
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- W2014798451 doi "https://doi.org/10.1214/aos/1176325380" @default.
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