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1 by Iosif Pinelis We consider Hotelling's T 2 statistic for an arbitrary d-dimensional sample. If the sampling is not too deterministic or inhomogeneous, then under zero means hypothesis, T 2 tends to χ 2 d in distribution. We are showing that a test for the orthant symmetry condition introduced by Efron can be constructed which does not essentially differ(More)
(A) Closed and bounded centrally symmetric sets S in E n can also be characterized by the property that for each n-dimensional simplex T with vertices in S there is a translate of −T also having its vertices in S. This, of course, is a consequence of Theorem 1, since the three-point sets belonging to S are subsets of the (n + 1)-point sets with vertices in(More)
Let BS 1 ,. .. , BSn be independent identically distributed random variables each having the standardized Bernoulli distribution with parameter p ∈ (0, 1). Let m * (p) := (1 + p + 2 p 2)/(2 p − p 2 + 4 p 2) if 0 < p 1 2 and m * (p) := 1 if 1 2 p < 1. Let m m * (p). Let f be such a function that f and f ′′ are nondecreasing and convex. Then it is proved that(More)