Open Access
September, 1981 Total Positivity Properties of Absolute Value Multinormal Variables with Applications to Confidence Interval Estimates and Related Probabilistic Inequalities
Samuel Karlin, Yosef Rinott
Ann. Statist. 9(5): 1035-1049 (September, 1981). DOI: 10.1214/aos/1176345583

Abstract

Total positivity properties of multivariate densities are useful in deducing positive dependence of random vector components and related probability inequalities. In this paper we determine necessary and sufficient conditions for total positivity of absolute value multinormal variables. The results are applied to obtain positive dependence and associated inequalities for the multinormal and related distributions, e.g., the multivariate $t$ and Wishart distributions. Inequalities of this type yield bounds for multivariate confidence set probabilities.

Citation

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Samuel Karlin. Yosef Rinott. "Total Positivity Properties of Absolute Value Multinormal Variables with Applications to Confidence Interval Estimates and Related Probabilistic Inequalities." Ann. Statist. 9 (5) 1035 - 1049, September, 1981. https://doi.org/10.1214/aos/1176345583

Information

Published: September, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0477.62035
MathSciNet: MR628759
Digital Object Identifier: 10.1214/aos/1176345583

Subjects:
Primary: 62H05

Keywords: association , Correlation inequalities , multivariate $t$ distribution , multivariate normal distribution , total positivity , Wishart distribution

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 5 • September, 1981
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