相关论文: A technical note on divergence of the Wald statist…
In this note a two sided bound on the tail probability of sums of independent, and either symmetric or nonnegative, random variables is obtained. We utilize a recent result by Lata{\l}a on bounds on moments of such sums. We also give a new…
This article focuses on linear eigenvalue statistics of Hankel matrices with independent entries. Using the convergence of moments we show that the linear eigenvalue statistics of Hankel matrices for odd degree monomials with degree greater…
In an attempt to progress towards proving the conjecture the numerical range W (A) is a 2--spectral set for the matrix A, we propose a study of various constants. We review some partial results, many problems are still open. We describe our…
We test against two different sets of data an apparently new approach to the analysis of the variance of a numerical variable which depends on qualitative characters. We suggest that this approach be used to complement other existing…
This study investigates a powerful model, targeted to subjective assessments, based on pairwise comparisons. It provides a proof that a distance-based inconsistency reduction transforms an inconsistent pairwise comparisons (PC) matrix into…
We study the defect (or "signed area") distribution of toral Laplace eigenfunctions restricted to shrinking balls of radius above the Planck scale, in either random Gaussian scenario ("Arithmetic Random Waves"), or deterministic…
Asymptotic properties of the local Whittle estimator in the nonstationary case (d>{1/2}) are explored. For {1/2}<d\leq 1, the estimator is shown to be consistent, and its limit distribution and the rate of convergence depend on the value of…
Randomly censored survival data are frequently encountered in applied sciences including biomedical or reliability applications and clinical trial analyses. Testing the significance of statistical hypotheses is crucial in such analyses to…
Recent theorems of Dubickas and Mossinghoff use auxiliary polynomials to give lower bounds on the Weil height of an algebraic number $\alpha$ under certain assumptions on $\alpha$. We prove a theorem which introduces an auxiliary polynomial…
We obtain several norm and eigenvalue inequalities for positive matrices partitioned into four blocks. The results involve the numerical range of the off-diagonal block X, especially the distance from 0 to W(X).
We derive the tail inequalities between two random variables starting from inequalities between its moment, or more generally between its Lebesgue-Riesz norms, which holds true on certain sets of parameters. We consider some applications…
In this article, we establish a near-optimal convergence rate for the CLT of linear eigenvalue statistics of Wigner matrices, in Kolmogorov-Smirnov distance. For all test functions $f\in C^5(\mathbb R)$, we show that the convergence rate is…
In this note, we derive a Leibniz rule for difference quotient.
Score-based tests have been used to study parameter heterogeneity across many types of statistical models. This chapter describes a new self-normalization approach for score-based tests of mixed models, which addresses situations where…
In this paper, we investigate condition numbers of eigenvalue problems of matrix polynomials with nonsingular leading coefficients, generalizing classical results of matrix perturbation theory. We provide a relation between the condition…
This work is concerned with finite range bounds on the variance of individual eigenvalues of Wigner random matrices, in the bulk and at the edge of the spectrum, as well as for some intermediate eigenvalues. Relying on the GUE example,…
We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus…
Several well-known results from the random matrix theory, such as Wigner's law and the Marchenko--Pastur law, can be interpreted (and proved) in terms of non-backtracking walks on a certain graph. Orthogonal polynomials with respect to the…
It is well known that the product of two independent regularly varying random variables with the same tail index is again regularly varying with this index. In this paper, we provide sharp sufficient conditions for the regular variation…
This article considers to model large-dimensional matrix time series by introducing a regression term to the matrix factor model. This is an extension of classic matrix factor model to incorporate the information of known factors or useful…