TY - JOUR
T1 - Covariance between variables and their order statistics for multivariate normal variables
AU - Rinott, Yosef
AU - Samuel-Cahn, Ester
PY - 1994/9/23
Y1 - 1994/9/23
N2 - Siegel (1993, J. Amer. Statist. Assoc. 88, 77-80) showed that when (X1, ..., Xn) have a multivariate normal distribution then Cov(X1, X(1)) = Σni = 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.
AB - Siegel (1993, J. Amer. Statist. Assoc. 88, 77-80) showed that when (X1, ..., Xn) have a multivariate normal distribution then Cov(X1, X(1)) = Σni = 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.
KW - Multivariate normal
KW - Order statistics
UR - http://www.scopus.com/inward/record.url?scp=0000389665&partnerID=8YFLogxK
U2 - 10.1016/0167-7152(94)90223-2
DO - 10.1016/0167-7152(94)90223-2
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AN - SCOPUS:0000389665
SN - 0167-7152
VL - 21
SP - 153
EP - 155
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
IS - 2
ER -