Related papers: Asymptotic Freeness for Rectangular Random Matrice…
Large-margin classifiers are popular methods for classification. We derive the asymptotic expression for the generalization error of a family of large-margin classifiers in the limit of both sample size $n$ and dimension $p$ going to…
We consider covariance asymptotics for linear statistics of general stationary random measures in terms of their truncated pair correlation measure. We give exact infinite series-expansion formulas for covariance of smooth statistics of…
For symmetric random matrices with correlated entries, which are functions of independent random variables, we show that the asymptotic behavior of the empirical eigenvalue distribution can be obtained by analyzing a Gaussian matrix with…
We show that finite rank perturbations of certain random matrices fit in the framework of infinitesimal (type B) asymptotic freeness. This can be used to explain the appearance of free harmonic analysis (such as subordination functions…
We consider large non-Hermitian random matrices $X$ with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having…
For sequences of non-lattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit of Edgeworth…
We propose a general framework for nonasymptotic covariance matrix estimation making use of concentration inequality-based confidence sets. We specify this framework for the estimation of large sparse covariance matrices through…
We consider the problem of detecting the presence of a submatrix with larger-than-usual values in a large data matrix. This problem was considered in (Butucea and Ingster, 2013) under a one-parameter exponential family, and one of the test…
We study the empirical measure associated to a sample of size $n$ and modified by $N$ iterations of the raking-ratio method. This empirical measure is adjusted to match the true probability of sets in a finite partition which changes each…
In this article we consider Wigner matrices $X_N$ with variance profiles (also called Wigner-type matrices) which are of the form $X_N(i,j) = \sigma(i/N,j/N) a_{i,j} / \sqrt{N}$ where $\sigma$ is a symmetric real positive function of…
We consider a general class of statistical experiments, in which an $n$-dimensional centered Gaussian random variable is observed and its covariance matrix is the parameter of interest. The covariance matrix is assumed to be…
We give simple criteria to identify the exponential order of magnitude of the absolute value of the determinant for wide classes of random matrix models, not requiring the assumption of invariance. These include Gaussian matrices with…
We study limit distributions of independent random matrices as well as limit joint distributions of their blocks under normalized partial traces composed with classical expectation. In particular, we are concerned with the ensemble of…
This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…
We derive new and improved non-asymptotic deviation inequalities for the sample average approximation (SAA) of an optimization problem. Our results give strong error probability bounds that are "sub-Gaussian"~even when the randomness of the…
The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we analyze the distribution of norms of complex Gaussian…
We prove deviation inequalities for sums of high-dimensional random matrices and operators with dependence and {\rc heavy tails}. Estimation of high-dimensional matrices is a concern for numerous modern applications. However, most results…
We study sample covariance matrices arising from rectangular random matrices with i.i.d. columns. It was previously known that the resolvent of these matrices admits a deterministic equivalent when the spectral parameter stays bounded away…
In the current paper we consider a Wigner matrix and consider an analytic function of polynomial growth on a set containing the support of the semicircular law in its interior. We prove that the linear spectral statistics corresponding to…
In this paper, we consider the empirical spectral distribution of the sample correlation matrix and investigate its asymptotic behavior under mild assumptions on the data's distribution, when dimension and sample size increase at the same…