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.
Keywords
MathematicsWishart distributionMultivariate statisticsStatisticsNormal-Wishart distributionConfidence intervalRandom variableMultivariate normal distributionApplied mathematicsEconometrics
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Publication Info
- Year
- 1981
- Type
- article
- Volume
- 9
- Issue
- 5
- Citations
- 95
- Access
- Closed
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Cite This
Samuel Karlin,
Yosef Rinott
(1981).
Total Positivity Properties of Absolute Value Multinormal Variables with Applications to Confidence Interval Estimates and Related Probabilistic Inequalities.
The Annals of Statistics
, 9
(5)
.
https://doi.org/10.1214/aos/1176345583
Identifiers
- DOI
- 10.1214/aos/1176345583