Related papers: Finite Dimensional Statistical Inference

Consider a deterministic self-adjoint matrix X_n with spectral measure converging to a compactly supported probability measure, the largest and smallest eigenvalues converging to the edges of the limiting measure. We perturb this matrix by…

This paper is devoted to the study of the eigenvalues of the Wishart process which are the analogof the Dyson Brownian Motion for covariance matrices. Such processes were in particular studied byBru. The mean field convergence of the…

In this paper we derive some new and practical results on testing and interval estimation problems for the population eigenvalues of a Wishart matrix based on the asymptotic theory for block-wise infinite dispersion of the population…

Since their initial introduction, score-based diffusion models (SDMs) have been successfully applied to solve a variety of linear inverse problems in finite-dimensional vector spaces due to their ability to efficiently approximate the…

Statistical inference as a formal scientific method to covert experience to knowledge has proven to be elusively difficult. While frequentist and Bayesian methodologies have been accepted in the contemporary era as two dominant schools of…

We here provide a distribution-free approach to the random factor analysis model. We show that it leads to the same estimating equations as for the classical ML estimates under normality, but more easily derived, and valid also in the case…

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

Let $F=F_N$ be the distribution of a finite real population of size $N$. Let $\widehat{F}=F_N$ be the empirical distribution of a sample of size $n$ drawn from the population without replacement. We prove the following remarkable {\it…

Let W be a Wishart random matrix of size d^2 times d^2, considered as a block matrix with d times d blocks. Let Y be the matrix obtained by transposing each block of W. We prove that the empirical eigenvalue distribution of Y approaches a…

Covariance matrix estimation arises in multivariate problems including multivariate normal sampling models and regression models where random effects are jointly modeled, e.g. random-intercept, random-slope models. A Bayesian analysis of…

We compute analytically the probability distribution and moments of the sum and product of the non-zero eigenvalues and singular values of random matrices with (i) non-negative entries, (ii) fixed rank, and (iii) prescribed sums of the…

For the correlated Gaussian Wishart ensemble we compute the distribution of the smallest eigenvalue and a related gap probability.We obtain exact results for the complex (\beta=2) and for the real case (\beta=1). For a particular set of…

We developed a statistical inference method applicable to a broad range of generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients scales proportionally with the sample size. Although a…

Let A be a p-variate real Wishart matrix on n degrees of freedom with identity covariance. The distribution of the largest eigenvalue in A has important applications in multivariate statistics. Consider the asymptotics when p grows in…

Assume a finite set of complex random variables form a determinantal point process, we obtain a theorem on the limit of the empirical distribution of these random variables. The result is applied to %We study the limits of the empirical…

Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…

By using a symbolic method, known in the literature as the classical umbral calculus, the trace of a non-central Wishart random matrix is represented as the convolution of the trace of its central component and of a formal variable…

Recent studies show that transformer-based architectures emulate gradient descent during a forward pass, contributing to in-context learning capabilities - an ability where the model adapts to new tasks based on a sequence of prompt…

We consider the problem of constructing confidence intervals for the locations of change points in a high-dimensional mean shift model. To that end, we develop a locally refitted least squares estimator and obtain component-wise and…

Let $X^{(\delta)}$ be a Wishart process of dimension $\delta$, with values in the set of positive matrices of size $m$. We are interested in the large deviations for a family of matrix-valued processes $\{\delta^{-1} X_t^{(\delta)}, t \leq…