相关论文: High Dimensional Statistical Inference and Random …

Estimating large covariance and precision matrices are fundamental in modern multivariate analysis. The problems arise from statistical analysis of large panel economics and finance data. The covariance matrix reveals marginal correlations…

We present a brief overview of random matrix theory (RMT) with the objectives of highlighting the computational results and applications in financial markets as complex systems. An oft-encountered problem in computational finance is the…

This article is due to appear in the Handbook of Statistics, Vol. 43, Elsevier/North-Holland, Amsterdam, edited by Arni S. R. Srinivasa Rao and C. R. Rao. In modern day analytics, there is ever growing need to develop statistical models to…

Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the…

Statistical inference is the science of drawing conclusions about some system from data. In modern signal processing and machine learning, inference is done in very high dimension: very many unknown characteristics about the system have to…

Current statistical inference problems in areas like astronomy, genomics, and marketing routinely involve the simultaneous testing of thousands -- even millions -- of null hypotheses. For high-dimensional multivariate distributions, these…

Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed. We trace this consistency to a simple linear effect: the shared Gaussian statistics across…

We study complex networks under random matrix theory (RMT) framework. Using nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the eigenvalues of adjacency matrix of various model networks, namely, random,…

A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…

Despite of various similar features, Functional Data Analysis and High-Dimensional Data Analysis are two major fields in Statistics that grew up recently almost independently one from each other. The aim of this paper is to propose a survey…

The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…

In this short note we collect together known results on the use of Random Matrix Theory in lattice statistical mechanics. The purpose here is two fold. Firstly the RMT analysis provides an intrinsic characterization of integrability, and…

Though the statistical analysis of ranking data has been a subject of interest over the past centuries, especially in economics, psychology or social choice theory, it has been revitalized in the past 15 years by recent applications such as…

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…

Multivariate spatially-oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for…

The Random Parameters model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we…

Studies often estimate associations between an outcome and multiple variates. For example, studies of diagnostic test accuracy estimate sensitivity and specificity, and studies of predictive and prognostic factors typically estimate…

Data-driven approaches, when tasked with situation awareness, are suitable for complex grids with massive datasets. It is a challenge, however, to efficiently turn these massive datasets into useful big data analytics. To address such a…

For a long time, detection and parameter estimation methods for signal processing have relied on asymptotic statistics as the number $n$ of observations of a population grows large comparatively to the population size $N$, i.e. $n/N\to…

Stochastic dominance is an important concept in probability theory, econometrics and social choice theory for robustly modeling agents' preferences between random outcomes. While many works have been dedicated to the univariate case, little…