Total positivity properties of absolute value multinormal variables with applications to confidence interval estimates and related probabilistic inequalities
From MaRDI portal
Publication:1161010
DOI10.1214/aos/1176345583zbMath0477.62035OpenAlexW2071521616MaRDI QIDQ1161010
Publication date: 1981
Published in: The Annals of Statistics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1214/aos/1176345583
correlation inequalitiesWishart distributionassociationmultivariate t distributionmultivariate normal distribution
Measures of association (correlation, canonical correlation, etc.) (62H20) Characterization and structure theory for multivariate probability distributions; copulas (62H05)
Related Items
Tchebycheff-Experiments ⋮ Association and infinite divisibility for the Wishart distribution and its diagonal marginals ⋮ Approximating boundary crosing probabilities with applications to sequential tests ⋮ Extensions of multiple testing procedures based on Simes' test ⋮ Testing the equality of multivariate means when \(p>n\) by combining the Hotelling and Simes tests ⋮ Developments on \(\text{MTP}_2\) properties of absolute value multinormal variables with nonzero means. ⋮ Sign regularity of a generalized Cauchy kernel with applications ⋮ A combinatorial proof of the Gaussian product inequality beyond the \(\mathrm{MTP}_2\) case ⋮ Stochastic comparisons of order statistics and their concomitants ⋮ On the Simes test under dependence ⋮ A short proof of a strong form of the three dimensional Gaussian product inequality ⋮ Quantitative versions of the two-dimensional Gaussian product inequalities ⋮ Optimal rates for estimation of two-dimensional totally positive distributions ⋮ Statistical proofs of some matrix results ⋮ Product inequalities for multivariate Gaussian, gamma, and positively upper orthant dependent distributions ⋮ A Gaussian inequality for expected absolute products ⋮ On a class of prior distributions that accounts for uncertainty in the data ⋮ Miscellaneous results related to the Gaussian product inequality conjecture for the joint distribution of traces of Wishart matrices ⋮ Portfolio selection through an extremality stochastic order ⋮ Characterization of positively correlated squared Gaussian processes ⋮ Representations of the absolute value function and applications in Gaussian estimates ⋮ Properties of a job search problem on a partially observable Markov chain in a dynamic economy ⋮ Inference about comparative precision in linear structural relationships ⋮ Copulas, uncertainty, and false discovery rate control ⋮ Non-exchangeable copulas and multivariate total positivity ⋮ Some probability inequalities for ordered MTP\(_2\) random variables: a proof of the Simes conjecture ⋮ The three-dimensional Gaussian product inequality ⋮ On a new class of multivariate prior distributions: theory and application in reliability ⋮ Simultaneous prediction intervals for multiple forecasts based on Bonferroni and product-type inequalities ⋮ Some percolations involving the Gaussian free fields ⋮ Maximum likelihood estimation in Gaussian models under total positivity ⋮ Stochastic order for alpha-permanental point processes ⋮ A note on the monotonicity of the critical values of a step-up test ⋮ An opposite Gaussian product inequality ⋮ A Bayesian positive dependence of survival times based on the multivariate arrangement increasing property ⋮ The control of the false discovery rate in multiple testing under dependency. ⋮ M-matrices as covariance matrices of multinormal distributions ⋮ New procedures controlling the false discovery proportion via Romano-Wolf's heuristic