Statistical Tests Based on Permutations of the Observations

Wald, A.; Wolfowitz, J.

doi:10.1214/aoms/1177731207

Cited by 260Probability and Statistical ResearchStatistical Methods and InferenceAdvanced Statistical Methods and Models

Statistical Tests Based on Permutations of the Observations

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Wald, A., Wolfowitz, J.·1944·The Annals of Mathematical Statistics

DOI 10.1214/aoms/1177731207

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In the scenario of large-scale problems, the distribution of eigenvalues tends to converge to a normal distribution.
“In the scenario of large-scale problems, the distribution of eigenvalues tends to converge to a normal distribution 42 .”
From Toward a linear-ramp QAOA protocol: evidence of a scaling advantage in solving some combinatorial optimization problems (2025) · cites this paper as [42]
The paper describes normal limiting distributions for permutation statistics and joint distributions of variates (Columbia University, pp. 12–14), not for eigenvalues. A search for eigenvalues and matrix characteristic roots found no passage addressing the claimed eigenvalue distribution. (LLM, conf=0.76)
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[1][1] A. WALD AND J. WoLFOwITz, Annals of Math. Stat., Vol. 14 (1943), p. 378. -
[2][2] HENRY ScHEFFÉ, Annals of Math. Stat., Vol. 14 (1943), p. 305. -
[3][3] H. HoTELLING AND M. R. PABST, Annals of Math. Stat., Vol. 7 (1936), p. 29. -
[4][4] E. J. G. PITmAN, Supp. Jour. Roy. Stat. Soc., Vol. 4 (1937), p. 225. -
[5][5] E. J. G. PitmaN, Supp. Jour. Roy. Stat. Soc., Vol. 4 (1937), p. 119. -
[6][6] E. J. G. PITMAN, Biometrika, Vol. 29 (1938), p. 322. -
[7][7] B. L. WELcí, Biometrika, Vol. 29 (1937), p. 21. -
[10][10] H. HoTELLING, Annals Math. Stat., Vol. 2 (1931), p. 359. -
[11][11] H. CRAmÉR AND H. WoLD, Journal London Math. Soc., Vol. 11 (1936), pp. 290–4. -
[12][12] J. RADoN, Sitzungsberichte Akademie Wien, Vol. 122 (1913), pp. 1295–1438. -

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Authors: Wald, A., & Wolfowitz, J.
Venue: The Annals of Mathematical Statistics
Publisher: Institute of Mathematical Statistics
Published: 1944-12
Volume: 15
Issue: 4
Pages: 358-372
ISSN: 0003-4851 (ISSN-L)
DOI: 10.1214/aoms/1177731207
OpenAlex: W2038298134
Cited by: 260
References: 4
Citations by year: 2026: 1 · 2025: 5 · 2024: 4 · 2023: 7 · 2022: 2 · 2021: 8 · 2020: 6 · 2019: 8 · 2018: 6 · 2017: 3 · 2016: 5 · 2015: 8 · 2014: 18 · 2013: 4 · 2012: 18
FWCI: 3.53
Type: journal article
Language: en
Open access: bronze
doi.org
Locations: The Annals of Mathematical Statistics (publishedVersion)
Project Euclid (Cornell University) (submittedVersion)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
Keywords: permutation tests, nonparametric tests, rank tests, asymptotic distribution, asymptotic normality, asymptotic efficiency

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