Concentration of measure and spectra of random matrices: Applications to correlation matrices, elliptical distributions and beyond
نویسندگان
چکیده
منابع مشابه
Concentration of measure and spectra of random matrices: with applications to correlation matrices, elliptical distributions and beyond
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. More formally we study the asymptotic properties of correlation and covariance matrices under the setting that p/n→ ρ ∈ (0,∞), for general population covariance. We show that spectral properties f...
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The usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants. From this representation one can deduce formulas for spacing probabilities in terms of Fredholm determinants of matrix-valued kernels. The derivations of the various formulas are somewhat involved. In this article we present a direct approach which leads immediate...
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where Y ∈ Rp×n is a rectangular p×n matrix with random centered entries, and both n and p ≤ n tend to infinity: typically p = p(n), and p(n)/n tends to some limit. M can be seen as the empirical covariance matrix of a random vector of dimension p sampled n times, each sample being a column of Y . It is common in applications to have a number of variables with a comparable order of magnitude wit...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2009
ISSN: 1050-5164
DOI: 10.1214/08-aap548