264 research outputs found
Partial stochastic dominance for the multivariate Gaussian distribution
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.Comment: 7 page
Tusnady's inequality revisited
Tusnady's inequality is the key ingredient in the KMT/Hungarian coupling of
the empirical distribution function with a Brownian bridge. We present an
elementary proof of a result that sharpens the Tusnady inequality, modulo
constants. Our method uses the beta integral representation of Binomial tails,
simple Taylor expansion and some novel bounds for the ratios of normal tail
probabilities.Comment: Published at http://dx.doi.org/10.1214/009053604000000733 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
- …