A reverse Gaussian correlation inequality by adding cones

作者：Chen Xiaohong; Gao Fuchang^*

来源：Statistics & Probability Letters, 2017, 123: 84-87.

DOI：10.1016/j.spl.2016.11.031

• Gaussian measure
• Convex set
• Convex cone
• Posterior distribution
• Likelihood ratio
• Chi-bar distribution

Let gamma denote any centered Gaussian measure on R-d. It is proved that for any closed convex sets A and B in R-d, and any closed convex cones C and Din R-d, if D superset of C degrees, where C degrees is the polar cone of C, then
gamma ((A + C) boolean AND (B + D)) <= gamma (A + C) . gamma (B + D),
and
gamma ((A +C) boolean AND (B - D)) >= (A + C) . gamma (B - D).
As an application, this new inequality is used to bound the asymptotic posterior distributions of likelihood ratio statistics for convex cones.

• 出版日期2017-4