On Gaussian correlation inequalities for "periodic" sets

Subir K. Bhandari and Ayanendranath Basu

Statistics & Probability Letters, 2005, vol. 73, issue 3, 315-320

Abstract: Let A and B be convex sets in containing the origin which are invariant under rotation around the origin by a 2[pi]/k angle, k=2,3,4,5,... . In this paper we establish the correlation inequality P(A[intersection]B)[greater-or-equal, slanted]P(A)P(B) under the N2(0,I2) distribution of X, for sets A and B as described above. This provides a generalization of Pitt's [1977. Ann. Probab. 5, 470-474] result, which established this correlation inequality for the case k=2, i.e. for convex symmetric sets.

Keywords: Correlation; inequality; Periodic; functions (search for similar items in EconPapers)
Date: 2005
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