Some limit theorems for the eigenvalues of a sample covariance matrix
TLDR
The limit of the cumulative distribution function of the eigenvalues is determined by use of a method of moments as discussed by the authors, which is mainly combinatorial, and it is shown that the sum of eigen values, raised to k -th power, k = 1, 2, 3, 4, 5, 6, m is asymptotically normal.About:
This article is published in Journal of Multivariate Analysis.The article was published on 1982-03-01 and is currently open access. It has received 410 citations till now. The article focuses on the topics: Matrix differential equation & Spectrum of a matrix.read more
Citations
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From theory to practice: an overview of MIMO space-time coded wireless systems
TL;DR: An overview of progress in the area of multiple input multiple output (MIMO) space-time coded wireless systems is presented and the state of the art in channel modeling and measurements is presented, leading to a better understanding of actual MIMO gains.
Book
Random Matrix Theory and Wireless Communications
Antonio M. Tulino,Sergio Verdu +1 more
TL;DR: A tutorial on random matrices is provided which provides an overview of the theory and brings together in one source the most significant results recently obtained.
Book
An Introduction to Random Matrices
TL;DR: The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic and combinatorial) as mentioned in this paper.
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Topics in Random Matrix Theory
TL;DR: The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics as mentioned in this paper, which makes the current state of the field almost too large to survey in a single book.
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Fixed-Point Continuation for $\ell_1$-Minimization: Methodology and Convergence
Elaine Hale,Wotao Yin,Yin Zhang +2 more
TL;DR: The structure of optimal solution sets is studied, finite convergence for important quantities is proved, and $q$-linear convergence rates for the fixed-point algorithm applied to problems with $f(x)$ convex, but not necessarily strictly convex are established.
References
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Book
An Introduction to Multivariate Statistical Analysis
TL;DR: In this article, the distribution of the Mean Vector and the Covariance Matrix and the Generalized T2-Statistic is analyzed. But the distribution is not shown to be independent of sets of Variates.
Book
Linear statistical inference and its applications
TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
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Introduction to Multivariate Statistical Analysis.
William G. Madow,T. W. Anderson +1 more