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A reverse Gaussian correlation inequality by adding cones

Author

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  • Chen, Xiaohong
  • Gao, Fuchang
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.

Suggested Citation

  • Chen, Xiaohong & Gao, Fuchang, 2017. "A reverse Gaussian correlation inequality by adding cones," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 84-87.
    • Handle: RePEc:eee:stapro:v:123:y:2017:i:c:p:84-87
    DOI: 10.1016/j.spl.2016.11.031
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    References listed on IDEAS

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    1. Xiaohong Chen & Timothy Christensen & Elie Tamer, 2016. "MCMC Confidence sets for Identified Sets," Cowles Foundation Discussion Papers 2037, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. Xiaohong Chen & Timothy M. Christensen & Elie Tamer, 2018. "Monte Carlo Confidence Sets for Identified Sets," Econometrica, Econometric Society, vol. 86(6), pages 1965-2018, November.
    2. Xiaohong Chen & Timothy M. Christensen & Elie Tamer, 2017. "Monte Carlo confidence sets for identified sets," CeMMAP working papers 43/17, Institute for Fiscal Studies.

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