Related papers: Large dimension forecasting models and random sing…
High-dimensional data sets are commonly collected in many contemporary applications arising in various fields of scientific research. We present two views of finite samples in high dimensions: a probabilistic one and a nonprobabilistic one.…
In this paper, we show that the diagonal of a high-dimensional sample covariance matrix stemming from $n$ independent observations of a $p$-dimensional time series with finite fourth moments can be approximated in spectral norm by the…
This paper is concerned with extensions of the classical Mar\v{c}enko-Pastur law to time series. Specifically, $p$-dimensional linear processes are considered which are built from innovation vectors with independent, identically distributed…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
The asymptotic behaviour of Linear Spectral Statistics (LSS) of the smoothed periodogram estimator of the spectral coherency matrix of a complex Gaussian high-dimensional time series $(\y_n)_{n \in \mathbb{Z}}$ with independent components…
We derive the Marchenko-Pastur (MP) law for sample covariance matrices of the form $V_n=\frac{1}{n}XX^T$, where $X$ is a $p\times n$ data matrix and $p/n\to y\in(0,\infty)$ as $n,p \to \infty$. We assume the data in $X$ stems from a…
When can reliable inference be drawn in the "Big Data" context? This paper presents a framework for answering this fundamental question in the context of correlation mining, with implications for general large scale inference. In large…
We consider the singular values of certain Young diagram shaped random matrices. For block-shaped random matrices, the empirical distribution of the squares of the singular eigenvalues converges almost surely to a distribution whose moments…
We apply the method of determinants to study the distribution of the largest singular values of large $ m \times n $ real rectangular random matrices with independent Cauchy entries. We show that statistical properties of the (rescaled by a…
In this note we develop an extension of the Mar\v{c}enko-Pastur theorem to time series model with temporal correlations. The limiting spectral distribution (LSD) of the sample covariance matrix is characterised by an explicit equation for…
We show how random matrix theory can be applied to develop new algorithms to extract dynamic factors from macroeconomic time series. In particular, we consider a limit where the number of random variables N and the number of consecutive…
We obtain the limiting spectral distribution for large sample covariance matrices associated with random vectors having graph-dependent entries under the assumption that the interdependence among the entries grows with the sample size n.…
Time series datasets often contain heterogeneous signals, composed of both continuously changing quantities and discretely occurring events. The coupling between these measurements may provide insights into key underlying mechanisms of the…
High dimensional time series datasets are becoming increasingly common in various fields such as economics, finance, meteorology, and neuroscience. Given this ubiquity of time series data, it is surprising that very few works on variable…
We discuss the applications of Random Matrix Theory in the context of financial markets and econometric models, a topic about which a considerable number of papers have been devoted to in the last decade. This mini-review is intended to…
In statistics, assuming samples are independent is reasonable. However, this property can fail to hold for the features, a distinction that has led to several lines of work aiming to remove the latter assumption of independence present in…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
We show that, within a finite window of parameter space, random matrix theory (RMT) statistics emerge in observables of a finite-volume massive free scalar field theory after a local operator quench. The spacing-ratio distribution of…
We introduce a finite version of free probability for rectangular matrices that amounts to operations on singular values of polynomials. We show that we can replicate the transforms from free probability, and that asymptotically there is…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…