Association of Random Variables, with Applications
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Pitt's Gaussian correlation inequality gives the qualitative bound γW ≥ 0 but not a quantitative comparison to γ.
“Pitt's Gaussian correlation inequality (Pitt, 1977;Esary et al., 1967;Joag-Dev and Proschan, 1983) gives the qualitative bound γW ≥ 0 but not a quantitative comparison to γ, so direct estimation is the right move.”
From RoPoLL: Robust Panel of LLM Judges (2026) · cites this paper as Esary et al., 1967
Section 4.2 (p. 5) gives the qualitative result that association implies nonnegative covariance for nondecreasing functions. The paper does not identify this as Pitt’s Gaussian inequality, address the bound γW ≥ 0 in that notation, or compare γW quantitatively with γ. It therefore supports the general nonnegativity principle, but not the Gaussian-specific attribution. (LLM, conf=0.86)
Experimental — accuracy not yet measuredFor jointly Gaussian competent noise with positive score correlation, the cluster indicators are positively associated by Pitt's Gaussian correlation inequality, so γW ≥ 0.
“For jointly Gaussian competent noise with positive score correlation, the cluster indicators are positively associated by Pitt's Gaussian correlation inequality (Pitt, 1977;Esary et al., 1967;Joag-Dev and Proschan, 1983), so γW ≥ 0”
From RoPoLL: Robust Panel of LLM Judges (2026) · cites this paper as Esary et al., 1967
The paper’s section 4.1 (p. 5) establishes that two binary random variables are associated exactly when their covariance is nonnegative; p. 1 also states that nondecreasing functions of associated variables remain associated. These results support the association-to-nonnegative-covariance step, but our copy does not establish the Gaussian premise, discuss Pitt’s inequality, or identify γW with the indicators’ covariance. (LLM, conf=0.86)
Experimental — accuracy not yet measured
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Research works printed but not linked: 1
- [1][1] HARDY, G. H., LITTLEwooD, J. E. and PóLYA, G. (1934). Inequalities. Cambridge Univ. Press. -
Cited by
Sorted by citations
RoPoLL: Robust Panel of LLM Judges
Acharya, A., Pan, K. W., & Verkhovsky, B. (2026) · arXiv · doi:10.48550/arxiv.2606.30931
Online control of the familywise error rate
Tian, J., & Ramdas, A. (2019) · arXiv · doi:10.48550/arxiv.1910.04900 · Cited by 18
- Authors
- Esary, J. D., Proschan, F., & Walkup, D. W.
- Venue
- The Annals of Mathematical Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1967-10
- Volume
- 38
- Issue
- 5
- Pages
- 1466-1474
- ISSN
- 0003-4851
- Cited by
- 963
- References
- 0
- Language
- en
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