On information plus noise kernel random matrices
نویسندگان
چکیده
منابع مشابه
On information plus noise kernel random matrices
Kernel random matrices have attracted a lot of interest in recent years, from both practical and theoretical standpoints. Most of the theoretical work so far has focused on the case were the data is sampled from a low-dimensional structure. Very recently, the first results concerning kernel random matrices with high-dimensional input data were obtained, in a setting where the data was sampled f...
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Free probability and random matrix theory has shown to be a fruitful combination in many fields of research, such as digital communications, nuclear physics and mathematical finance. The link between free probability and eigenvalue distributions of random matrices will be strengthened further in this paper. It will be shown how the concept of multiplicative free convolution can be used to expre...
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Let Xn be n×N containing i.i.d. complex entries and unit variance (sum of variances of real and imaginary parts equals 1), σ > 0 constant, and Rn an n×N random matrix independent of Xn. Assume, almost surely, as n →∞, the empirical distribution function (e.d.f.) of the eigenvalues of 1 N RnR ∗ n converges in distribution to a nonrandom probability distribution function (p.d.f.), and the ratio n...
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We place ourselves in the setting of high-dimensional statistical inference, where the number of variables p in a dataset of interest is of the same order of magnitude as the number of observations n. We consider the spectrum of certain kernel random matrices, in particular n × n matrices whose (i, j)-th entry is f(X ′ iXj/p) or f(‖Xi − Xj‖/p), where p is the dimension of the data, and Xi are i...
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We consider a class of matrices of the form Cn = (1/N)(Rn+σXn)(Rn+σXn) ∗, where Xn is an n × N matrix consisting of independent standardized complex entries, Rj is an n×N nonrandom matrix, and σ > 0. Among several applications, Cn can be viewed as a sample correlation matrix, where information is contained in (1/N)RnR ∗ n, but each column of Rn is contaminated by noise. As n → ∞, if n/N → c > 0...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2010
ISSN: 0090-5364
DOI: 10.1214/10-aos801