The Annals of Statistics

Total Positivity Properties of Absolute Value Multinormal Variables with Applications to Confidence Interval Estimates and Related Probabilistic Inequalities

Samuel Karlin and Yosef Rinott

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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.

Article information

Source
Ann. Statist., Volume 9, Number 5 (1981), 1035-1049.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345583

Digital Object Identifier
doi:10.1214/aos/1176345583

Mathematical Reviews number (MathSciNet)
MR628759

Zentralblatt MATH identifier
0477.62035

JSTOR
links.jstor.org

Subjects
Primary: 62H05: Characterization and structure theory

Keywords
Total positivity association correlation inequalities multivariate normal distribution multivariate $t$ distribution Wishart distribution

Citation

Karlin, Samuel; Rinott, Yosef. Total Positivity Properties of Absolute Value Multinormal Variables with Applications to Confidence Interval Estimates and Related Probabilistic Inequalities. Ann. Statist. 9 (1981), no. 5, 1035--1049. doi:10.1214/aos/1176345583. https://projecteuclid.org/euclid.aos/1176345583


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