Related papers: Joint density of eigenvalues in spiked multivariat…
This paper aims to test the number of spikes in a generalized spiked covariance matrix, the spiked eigenvalues of which may be extremely larger or smaller than the non-spiked ones. For a high-dimensional problem, we first propose a general…
The eigenvalues of matrices representing the structure of large-scale complex networks present a wide range of applications, from the analysis of dynamical processes taking place in the network to spectral techniques aiming to rank the…
Random-effects meta-analyses are very commonly used in medical statistics. Recent methodological developments include multivariate (multiple outcomes) and network (multiple treatments) meta-analysis. Here we provide a new model and…
Principal loading analysis is a dimension reduction method that discards variables which have only a small distorting effect on the covariance matrix. We complement principal loading analysis and propose to rather use a mix of both, the…
Sparse PCA is a widely used technique for high-dimensional data analysis. In this paper, we propose a new method called low-rank principal eigenmatrix analysis. Different from sparse PCA, the dominant eigenvectors are allowed to be dense…
A methodology to analyze the properties of the first (largest) eigenvalue and its eigenvector is developed for large symmetric random sparse matrices utilizing the cavity method of statistical mechanics. Under a tree approximation, which is…
The aim of this paper is to establish several deep theoretical properties of principal component analysis for multiple-component spike covariance models. Our new results reveal a surprising asymptotic conical structure in critical sample…
Estimating the number of eigenvalues located in a given interval of a large sparse Hermitian matrix is an important problem in certain applications and it is a prerequisite of eigensolvers based on a divide-and-conquer paradigm. Often an…
Ideally, all analyses of normally distributed data should include the full covariance information between all data points. In practice, the full covariance matrix between all data points is not always available. Either because a result was…
Multivariate hypergeometric distribution arises frequently in elementary statistics and probability courses, for simultaneously studying the occurence law of specified events, when sampling without replacement from a finite population with…
Multivariate meta-analysis can be adapted to a wide range of situations for multiple outcomes and multiple treatment groups when combining studies together. The within-study correlation between effect sizes is often assumed known in…
Gene expression datasets are usually of high dimensionality and therefore require efficient and effective methods for identifying the relative importance of their attributes. Due to the huge size of the search space of the possible…
We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal…
We provide a new general theorem for multivariate normal approximation on convex sets. The theorem is formulated in terms of a multivariate extension of Stein couplings. We apply the results to a homogeneity test in dense random graphs and…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
This article proposes a generalized notion of extreme multivariate dependence between two random vectors which relies on the extremality of the cross-covariance matrix between these two vectors. Using a partial ordering on the…
We compute exact asymptotic of the statistical density of random matrices belonging to invariant random matrices ensemble (RMT) orthogonal, unitary and symplectic ensembles, where all its eigenvalues lie within the interval $[\sigma,…
As the meta-analysis of more than one diagnostic tests can impact clinical decision making and patient health, there is an increasing body of research in models and methods for meta-analysis of studies comparing multiple diagnostic tests.…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
The ensemble inter-relations to be considered are special features of classical cases, where the joint eigenvalue probability density can be computed explicitly. Attention will be focussed too on the consequences of these inter-relations,…