Covariance between variables and their order statistics for multivariate normal variables

Yosef Rinott and Ester Samuel-Cahn

Statistics & Probability Letters, 1994, vol. 21, issue 2, 153-155

Abstract: Siegel (1993, J. Amer. Statist. Assoc. 88, 77-80) showed that when (X1, ..., Xn) have a multivariate normal distribution then Cov(X1, X(1)) = [Sigma]ni = 1 Cov(X1, Xi)P(Xi = X(1)), where X(1) is the minimum of (X1, ..., Xn). We show that a similar result holds for any order statistic. Thus X(1) can be replaced by X(r), the rth order statistic, everywhere in the above formula. Normality is essentially also necessary for this result to hold.

Keywords: Multivariate; normal; Order; statistics (search for similar items in EconPapers)
Date: 1994
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Citations: View citations in EconPapers (2)

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