Covariance between variables and their order statistics for multivariate normal variables
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.
Year of publication: |
1994
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Authors: | Rinott, Yosef ; Samuel-Cahn, Ester |
Published in: |
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 21.1994, 2, p. 153-155
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Publisher: |
Elsevier |
Subject: | Multivariate normal Order statistics |
Saved in:
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