تقرير
On Wilks' joint moment formulas for embedded principal minors of Wishart random matrices
| العنوان: | On Wilks' joint moment formulas for embedded principal minors of Wishart random matrices |
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| المؤلفون: | Genest, Christian, Ouimet, Frédéric, Richards, Donald |
| المصدر: | Stat (2024), 13 (2), e706, 6 pp |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Statistics Theory, Mathematics - Probability, 62E15, 60E15, 62H10, 62H12 |
| الوصف: | In 1934, the American statistician Samuel S. Wilks derived remarkable formulas for the joint moments of embedded principal minors of sample covariance matrices in multivariate Gaussian populations, and he used them to compute the moments of sample statistics in various applications related to multivariate linear regression. These important but little-known moment results were extended in 1963 by the Australian statistician A. Graham Constantine using Bartlett's decomposition. In this note, a new proof of Wilks' results is derived using the concept of iterated Schur complements, thereby bypassing Bartlett's decomposition. Furthermore, Wilks' open problem of evaluating joint moments of disjoint principal minors of Wishart random matrices is related to the Gaussian product inequality conjecture. Comment: 6 pages, 0 figures |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1002/sta4.706 |
| URL الوصول: | http://arxiv.org/abs/2403.06330 |
| رقم الأكسشن: | edsarx.2403.06330 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1002/sta4.706 |
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