Partial stochastic dominance for the multivariate Gaussian distribution

Amanda Turner; John Whitehead

doi:10.1016/j.spl.2015.04.018

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arXiv · 1407.0936

Partial stochastic dominance for the multivariate Gaussian distribution

Amanda Turner·John Whitehead

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Abstract

Gaussian comparison inequalities provide a way of bounding probabilities relating to multivariate Gaussian random vectors in terms of probabilities of random variables with simpler correlation structures. In this paper, we establish the partial stochastic dominance result that the cumulative distribution function of the maximum of a multivariate normal random vector, with positive intraclass correlation coefficient, intersects the cumulative distribution function of a standard normal random variable at most once. This result can be applied to the Bayesian design of a clinical trial in which several experimental treatments are compared to a single control.

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Amanda Turner, John Whitehead. 2014-07-03. Partial stochastic dominance for the multivariate Gaussian distribution. https://doi.org/10.1016/j.spl.2015.04.018

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