相关论文: A technical note on divergence of the Wald statist…

We prove two estimates of the rate of convergence in the Lindeberg theorem, involving algebraic truncated third-order moments and the classical Lindeberg fraction, which generalize a series of inequalities due to (Esseen, 1969), (Rozovskii,…

As an application of Stein's method for Poisson approximation, we prove rates of convergence for the tail probabilities of two scan statistics that have been suggested for detecting local signals in sequences of independent random variables…

We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ points from an arbitrary probability measure in $\mathbf{R}^d$ relates to the wet part of that measure. This extends classical results for…

The Mann-Kendall test for trend has gained a lot of attention in a range of disciplines, especially in the environmental sciences. One of the drawbacks of the Mann-Kendall test when applied to real data is that no distinction can be made…

In order to adapt the Wasserstein distance to the large sample multivariate non-parametric two-sample problem, making its application computationally feasible, permutation tests based on the Sinkhorn divergence between probability vectors…

We prove that the the discrepancy of arithmetic progressions in the $d$-dimensional grid $\{1, \dots, N\}^d$ is within a constant factor depending only on $d$ of $N^{\frac{d}{2d+2}}$. This extends the case $d=1$, which is a celebrated…

Based on an apparently new Lagrange-type identity, a Cauchy--Schwarz-type inequality is proved. The mentioned identity is obtained by using certain ``macro'' variables; it is hoped that such a method can be used to prove or produce other…

In this note, we show that classical statistical tests for randomness are language dependent.

This paper deals with the problem of estimating the covariance matrix of a series of independent multivariate observations, in the case where the dimension of each observation is of the same order as the number of observations. Although…

We provide a template to derive convergence rates for the following popular versions of the Frank-Wolfe algorithm on polytopes: vanilla Frank-Wolfe, Frank-Wolfe with away steps, Frank-Wolfe with blended pairwise steps, and Frank-Wolfe with…

The study of several naturally arising "nearest neighbours" random walks benefits from the study of the associated orthogonal polynomials and their orthogonality measure. I consider extensions of this approach to a larger class of random…

We initiate the study of quadratic discrepancy for finite point sets on the Heisenberg group $\mathbb H^n$ with respect to upper Ahlfors regular probability measures. For a natural family of test sets given by left translations and…

We consider the empirical eigenvalue distribution of an $m\times m$ principal submatrix of an $n\times n$ random unitary matrix distributed according to Haar measure. For $n$ and $m$ large with $\frac{m}{n}=\alpha$, the empirical spectral…

We study the probability that a random polynomial with integer coefficients is reducible when factored over the rational numbers. Using computer-generated data, we investigate a number of different models, including both monic and non-monic…

In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root square mean, etc. Considering the difference of these means, we can establish. some inequalities among them. Interestingly, the difference of…

Latent variable models are well-known to suffer from rank deficiencies, causing problems with convergence and stability. Such problems are compounded in the "reduced-group split-ballot multitrait-multimethod model", which omits a set of…

We study the scaling of classification error rates with respect to the size of the training dataset. In contrast to classical results where rates are minimax optimal for a problem class, this work starts with the empirical observation that,…

The minimum rate needed to accurately approximate a product distribution based on an unnormalized informational divergence is shown to be a mutual information. This result subsumes results of Wyner on common information and Han-Verd\'{u} on…

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…

Consider $k$ independent random samples from $p$-dimensional multivariate normal distributions. We are interested in the limiting distribution of the log-likelihood ratio test statistics for testing for the equality of $k$ covariance…