Distribution of Eigenvalues of Sample Covariance Matrices with Tensor Product Samples
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Distribution of Eigenvalues of Sample Covariance Matrices with Tensor Product Samples
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| Creator |
Tieplova, D.
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| Description |
We consider the n² × n² real symmetric and hermitian matrices Mₙ, which are equal to the sum mn of tensor products of the vectors Xμ = B(Yμ ⊗ Yμ), μ = 1, . . . ,mn, where Yμ are i.i.d. random vectors from Rⁿ(Cⁿ) with zero mean and unit variance of components, and B is an n² × n² positive definite non-random matrix. We prove that if mₙ / n² → c ∊ [0,+∞) and the Normalized Counting Measure of eigenvalues of BJB, where J is defined below in (2.6), converges weakly, then the Normalized Counting Measure of eigenvalues of Mn converges weakly in probability to a non-random limit, and its Stieltjes transform can be found from a certain functional equation.
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| Date |
2018-07-10T17:04:04Z
2018-07-10T17:04:04Z 2017 |
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| Type |
Article
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| Identifier |
Distribution of Eigenvalues of Sample Covariance Matrices with Tensor Product Samples / D. Tieplova // Журнал математической физики, анализа, геометрии. — 2017. — Т. 13, № 1. — С. 82-98. — Бібліогр.: 11 назв. — англ.
1812-9471 DOI: doi.org/10.15407/mag13.01.082 Mathematics Subject Classification 2000: 15B52 http://dspace.nbuv.gov.ua/handle/123456789/140566 |
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| Language |
en
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| Relation |
Журнал математической физики, анализа, геометрии
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| Publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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