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Distributional approximations of (bi--) linear functions of sample variance-covariance matrices play a critical role to analyze vector time series, as they are needed for various purposes, especially to draw inference on the dependence…

Probability · Mathematics 2018-03-20 Ansgar Steland , Rainer von Sachs

In condensed-matter, level statistics has long been used to characterize the phases of a disordered system. We provide evidence within the context of a simple model that in a disordered large-N gauge theory with a gravity dual, there exist…

High Energy Physics - Theory · Physics 2012-06-12 Omid Saremi

Let $X\in \mathbb{R}^p$ and $Y\in \mathbb{R}$ be two random variables. We estimate the conditional covariance matrix $\mathrm{Cov}\left(\mathrm{E}\left[\boldsymbol{X}\vert Y\right]\right)$ applying a plug-in kernel-based algorithm to its…

Methodology · Statistics 2018-02-13 Jean-Michel Loubes , Clement Marteau , Maikol Solís

We compute spectra of sample auto-covariance matrices of second order stationary stochastic processes. We look at a limit in which both the matrix dimension $N$ and the sample size $M$ used to define empirical averages diverge, with their…

Disordered Systems and Neural Networks · Physics 2015-06-03 Reimer Kuehn , Peter Sollich

We prove a Poisson limit theorem in the total variation distance of functionals of a general Poisson point process using the Malliavin-Stein method. Our estimates only involve first and second order difference operators and are closely…

Probability · Mathematics 2019-05-28 Jens Grygierek

The stochastic gradient descent (SGD) algorithm has been widely used in statistical estimation for large-scale data due to its computational and memory efficiency. While most existing works focus on the convergence of the objective function…

Machine Learning · Statistics 2023-11-02 Xi Chen , Jason D. Lee , Xin T. Tong , Yichen Zhang

Sensitivity analysis in probabilistic discrete graphical models is usually conducted by varying one probability value at a time and observing how this affects output probabilities of interest. When one probability is varied then others are…

Statistics Theory · Mathematics 2021-01-14 Manuele Leonelli , Eva Riccomagno

We study the asymptotic behavior of stochastic hyperbolic parabolic equations with slow and fast time scales. Both the strong and weak convergence in the averaging principe are established, which can be viewed as a functional law of large…

Probability · Mathematics 2020-11-12 Michael Röckner , Longjie Xie , Li Yang

Statistical modeling of multivariate and spatial extreme events has attracted broad attention in various areas of science. Max-stable distributions and processes are the natural class of models for this purpose, and many parametric families…

Methodology · Statistics 2017-08-09 Clement Dombry , Sebastian Engelke , Marco Oesting

We establish some results for the rate of convergence in total variation of a Gibbs sampler to its equilibrium distribution. This sampler is motivated by a hierarchical Bayesian inference construction for a gamma random variable. Our…

Probability · Mathematics 2014-12-08 Oliver Jovanovski , Neal Madras

We consider learning methods based on the regularization of a convex empirical risk by a squared Hilbertian norm, a setting that includes linear predictors and non-linear predictors through positive-definite kernels. In order to go beyond…

Machine Learning · Computer Science 2019-06-19 Ulysse Marteau-Ferey , Dmitrii Ostrovskii , Francis Bach , Alessandro Rudi

This paper investigates the rate of convergence for the central limit theorem of linear spectral statistic (LSS) associated with large-dimensional sample covariance matrices. We consider matrices of the form ${\mathbf…

Probability · Mathematics 2025-06-05 Jian Cui , Jiang Hu , Zhidong Bai , Guorong Hu

We use the Stein-Chen method to study the extremal behaviour of the problem of extremes for univariate and bivariate geometric laws. We obtain a rate for the convergence to the Gumbel distribution of the law of the maximum of i. i. d.…

Probability · Mathematics 2015-10-27 Alessandra Cipriani , Anne Feidt

In this work, we propose new matrix- and tensor-based methodologies for estimating multivariate intensity functions of inhomogeneous point processes. By viewing multivariate intensity functions as infinite-dimensional matrices or tensors…

This paper deals with feature selection procedures for spatial point processes intensity estimation. We consider regularized versions of estimating equations based on Campbell theorem derived from two classical functions: Poisson likelihood…

Methodology · Statistics 2018-07-12 Achmad Choiruddin , Jean-François Coeurjolly , Frédérique Letué

A classical approach to accurately estimating the covariance matrix \Sigma of a p-variate normal distribution is to draw a sample of size n > p and form a sample covariance matrix. However, many modern applications operate with much smaller…

Statistics Theory · Mathematics 2014-03-05 Elizaveta Levina , Roman Vershynin

A minimal requirement for simulating multi-scale systems is to reproduce the statistical behavior of the slow variables. In particular, a good numerical method should accurately aproximate the probability density function of the…

Dynamical Systems · Mathematics 2018-04-13 J. Frank , G. A. Gottwald

Consider an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. In order to establish concentration properties for nonlinear functions $Z(A)$, it is standard to appeal to functional inequalities like Poincar\'e or…

Probability · Mathematics 2019-10-11 Mitia Duerinckx , Antoine Gloria

This paper introduces a family of recursively defined estimators of the parameters of a diffusion process. We use ideas of stochastic algorithms for the construction of the estimators. Asymptotic consistency of these estimators and…

Statistics Theory · Mathematics 2016-08-16 Jaime A. Londoño

Shape restrictions such as monotonicity on functions often arise naturally in statistical modeling. We consider a Bayesian approach to the problem of estimation of a monotone regression function and testing for monotonicity. We construct a…

Statistics Theory · Mathematics 2020-08-05 Moumita Chakraborty , Subhashis Ghosal