相关论文: E-values for k-Sample Tests With Exponential Famil…

In this paper, we study the problem of testing the equality of two multivariate distributions. One class of tests used for this purpose utilizes geometric graphs constructed using inter-point distances. So far, the asymptotic theory of…

This paper investigates a statistical procedure for testing the equality of two independently estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…

We deal with a general class of extreme-value regression models introduced by Barreto- Souza and Vasconcellos (2011). Our goal is to derive an adjusted likelihood ratio statistic that is approximately distributed as \c{hi}2 with a high…

We introduce Exponential Family Discriminant Analysis (EFDA), a unified generative framework that extends classical Linear Discriminant Analysis (LDA) beyond the Gaussian setting to any member of the exponential family. Under the assumption…

Exponential varieties arise from exponential families in statistics. These real algebraic varieties have strong positivity and convexity properties, familiar from toric varieties and their moment maps. Among them are varieties of inverses…

Analysis of low-degree polynomial algorithms is a powerful, newly-popular method for predicting computational thresholds in hypothesis testing problems. One limitation of current techniques for this analysis is their restriction to…

We give simple criteria to identify the exponential order of magnitude of the absolute value of the determinant for wide classes of random matrix models, not requiring the assumption of invariance. These include Gaussian matrices with…

In many families of distributions, maximum likelihood estimation is intractable because the normalization constant for the density which enters into the likelihood function is not easily available. The score matching estimator of…

In this article we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can be used to derive concentration inequalities in…

We consider the bulk eigenvalue statistics of Laplacian matrices of large Erd\H{o}s-R\'enyi random graphs in the regime $p \geq N^{\delta}/N$ for any fixed $\delta >0$. We prove a local law down to the optimal scale $\eta \gtrsim N^{-1}$…

In large scale multiple testing, the use of an empirical null distribution rather than the theoretical null distribution can be critical for correct inference. This paper proposes a ``mode matching'' method for fitting an empirical null…

Parameters defined via General Estimating Equations (GEE) can be estimated by maximizing the Empirical Likelihood (EL). Newey and Smith (2004) have recently shown that this EL estimator exhibits desirable higher-order asymptotic properties,…

Simultaneously testing $K$ hypotheses while controlling the family-wise error rate is a fundamental problem in statistics. Existing procedures (Bonferroni, Holm, Hochberg, Hommel) provide valid control but sacrifice power, increasingly so…

We examine the adjacency matrices of three-regular graphs representing one-face maps. Numerical studies reveal that the limiting eigenvalue statistics of these matrices are the same as those of much larger, and more widely studied classes…

This thesis studies high-dimensional, continuous-valued pairwise Markov Random Fields. We are particularly interested in approximating pairwise densities whose logarithm belongs to a Sobolev space. For this problem we propose the method of…

The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios…

The purpose of this note is to point out that the theory of expander graphs leads to an interesting test whether $n$ real numbers $x_1, \dots, x_n$ could be $n$ independent samples of a random variable. To any distinct, real numbers $x_1,…

We prove the almost sure invariance principle with rate $o(n^{\varepsilon})$ for every $\varepsilon > 0$ for H\"older continuous observables on nonuniformly expanding and nonuniformly hyperbolic transformations with exponential tails.…

The article considers an inhomogeneous Erd\H{o}s-R\"enyi random graph on $\{1,\ldots, N\}$, where an edge is placed between vertices $i$ and $j$ with probability $\varepsilon_N f(i/N,j/N)$, for $i\le j$, the choice being made independent…

We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter. The choice of $k$ depends on properties of each neighborhood, and therefore may…