相关论文: Large dimension forecasting models and random sing…
High-dimensional time series datasets are becoming increasingly common in many areas of biological and social sciences. Some important applications include gene regulatory network reconstruction using time course gene expression data, brain…
The Large Deviation Principle is established for stochastic models defined by past-dependent non linear recursions with small noise. In the Markov case we use the result to obtain an explicit expression for the asymptotics of exit time.
In this paper, we address the problem of testing independence between two high-dimensional random vectors. Our approach involves a series of max-sum tests based on three well-known classes of rank-based correlations. These correlation…
In this work we address the problem of approximating high-dimensional data with a low-dimensional representation. We make the following contributions. We propose an inverse regression method which exchanges the roles of input and response,…
A methodology for high dimensional causal inference in a time series context is introduced. It is assumed that there is a monotonic transformation of the data such that the dynamics of the transformed variables are described by a Gaussian…
We prove the convergence of the empirical spectral measure of Wishart matrices with size-dependent entries and characterize the limiting law by its moments. We apply our result to the cases where the entries are Bernoulli variables with…
Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to…
We present a simple yet rigorous approach to the determination of the spectral dimension of random trees, based on the study of the massless limit of the Gaussian model on such trees. As a byproduct, we obtain evidence in favor of a new…
We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of…
In the last decade, spectral linear statistics on large dimensional random matrices have attracted significant attention. Within the physics community, a privileged role has been played by invariant matrix ensembles for which a two…
A formalism for study of spectral correlations in non-Gaussian, unitary invariant ensembles of large random matrices with strong level confinement is reviewed. It is based on the Shohat method in the theory of orthogonal polynomials. The…
In this paper, we analyse singular values of a large $p\times n$ data matrix $\mathbf{X}_n= (\mathbf{x}_{n1},\ldots,\mathbf{x}_{nn})$ where the column $\mathbf{x}_{nj}$'s are independent $p$-dimensional vectors, possibly with different…
These lecture notes provide an overview of existing methodologies and recent developments for estimation and inference with high dimensional time series regression models. First, we present main limit theory results for high dimensional…
One popular approach for nonstructural economic and financial forecasting is to include a large number of economic and financial variables, which has been shown to lead to significant improvements for forecasting, for example, by the…
We analyze the extreme value dependence of independent, not necessarily identically distributed multivariate regularly varying random vectors. More specifically, we propose estimators of the spectral measure locally at some time point and…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using the Taylor expansion, is…
We use techniques from finite free probability to analyze matrix processes related to eigenvalues, singular values, and generalized singular values of random matrices. The models we use are quite basic and the analysis consists entirely of…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…
This paper considers linear model selection when the response is vector-valued and the predictors are randomly observed. We propose a new approach that decouples statistical inference from the selection step in a "post-inference model…
We consider the random matrix obtained by picking vectors randomly from a large collection of mutually unbiased bases of $\mathbb{C}^n$, and prove that the spectral distribution converges to the Marchenko-Pastur law. This shows that vectors…