MAXIMUM VARIANCE OF ORDER STATISTICS

NICKOS PAPADATOS

Department of Mathematics, Section of Statistics and Operations Research, University of Athens, Panepistemiopolis, 15784 Athens, Greece

(Received June 30, 1993; revised May 17, 1994)

Abstract. Yang (1982, Bull. Inst. Math. Acad. Sinica, 10(2), 197–204) proved that the variance of the sample median cannot exceed the population variance. In this paper, the upper bound for the variance of order statistics is derived, and it is shown that this is attained by Bernoulli variates only. The proof is based on Hoeffding’s identity for the covariance.

Key words and phrases: Variance bounds, order statistics, Bernoulli variates, Hoeffding’s identity.