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Order statistics in overlapping samples, moving order statistics and U-statistics

H. A. DAVID, Michael Philip Rogers

Open publisher page 12 citations

Abstract

Let X1, X2, … be a sequence of independent random variables with common distribution function F(x). Also let Xy:n(i) (i = 1,2, …) denote the rth order statistic in (Xi…, Xi+n−1). An expression is obtained for cov (Xr:n1(1), Xs:n2(n1 + 1-c)) in terms of the first two moments of order statistics in a sample of n'=n1+n2 −c drawn from F(x). This result is used to study the behaviour of order statistics in moving samples and to unify certain results for linear functions of order statistics expressible as U-statistics.

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What this paper is about

Let X1, X2, … be a sequence of independent random variables with common distribution function F(x). Also let Xy:n(i) (i = 1,2, …) denote the rth order statistic in (Xi…, Xi+n−1). An expression is obtained for cov (Xr:n1(1), Xs:n2(n1 + 1-c)) in terms of the first two moments of order statistics in a sample of n'=n1+n2 −c drawn from F(x). This result is used to study the behaviour of order statistics in moving samples and to unify certain results for linear functions of order statistics expressible as U-statistics.

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OpenAlex reports 12 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Let X1, X2, … be a sequence of independent random variables with common distribution function F(x). Also let Xy:n(i) (i = 1,2, …) denote the rth order statistic in (Xi…, Xi+n−1). An expression is obtained for cov (Xr:n1(1), Xs:n2(n1 + 1-c)) in terms of the first two moments of order statistics in a sample of n'=n1+n2 −c drawn from F(x). This result is used to study the behaviour of order statistics in moving samples and to unify certain results for linear functions of order statistics expressible as U-statistics.

Key concepts: Order statistic, Statistics, Mathematics, Statistic, Order (exchange), L-moment, Summary statistics, Generating function

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