# A reverse Gaussian correlation inequality by adding cones

*Xiaohong Chen* () and
*Fuchang Gao*

*Statistics & Probability Letters*, 2017, vol. 123, issue C, 84-87

**Abstract:**
Let γ denote any centered Gaussian measure on Rd. It is proved that for any closed convex sets A and B in Rd, and any closed convex cones C and D in Rd, if D⊇C∘, where C∘ is the polar cone of C, then γ((A+C)∩(B+D))≤γ(A+C)⋅γ(B+D), and γ((A+C)∩(B−D))≥γ(A+C)⋅γ(B−D). As an application, this new inequality is used to bound the asymptotic posterior distributions of likelihood ratio statistics for convex cones.

**Keywords:** Gaussian measure; Convex set; Convex cone; Posterior distribution; Likelihood ratio; Chi-bar distribution (search for similar items in EconPapers)

**Date:** 2017

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