Related papers: Bootstrap Consistency for Quadratic Forms of Sampl…

We bootstrap the $4$-point amplitude of $\mathcal{N}=2$ hypermultiplets in $\text{AdS}_2 \times \text{S}^2$ at tree-level and for arbitrary external weights. We hereby explicitly demonstrate the existence of a hidden four-dimensional…

We use the numerical conformal bootstrap to study six-dimensional $\mathcal{N}=(1,0)$ superconformal field theories with flavor symmetry $\mathfrak{so}_{4k}$. We present evidence that minimal $(D_k, D_k)$ conformal matter saturates the…

We derive non-asymptotic confidence regions for the mean of a random vector whose coordinates have an unknown dependence structure. The random vector is supposed to be either Gaussian or to have a symmetric bounded distribution, and we…

We obtain the $n$th centered moments of one level densities of a large orthogonal family of $L$-functions associated with holomorphic Hecke newforms of level $q$, averaged over $q\sim Q$. We verify the Katz-Sarnak conjecture for these…

The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio $s/d$, where $s$ and $d$ encode the…

We study the $n^{\rm th}$ centered moments of the $1$-level density for the low-lying zeros of $L$-functions attached to holomorphic cuspidal newforms of large prime level and fixed weight. Assuming the Generalized Riemann Hypotheses, we…

We propose a bootstrap-based test to detect a mean shift in a sequence of high-dimensional observations with unknown time-varying heteroscedasticity. The proposed test builds on the U-statistic based approach in Wang et al. (2022), targets…

Bootstrap techniques (also called resampling computation techniques) have introduced new advances in modeling and model evaluation. Using resampling methods to construct a series of new samples which are based on the original data set,…

Let $X,X_1,X_2,\ldots$ be i.i.d. ${\mathbb{R}}^d$-valued real random vectors. Assume that ${\mathbf{E}X=0}$, $\operatorname {cov}X=\mathbb{C}$, $\mathbf{E}\Vert X\Vert^2=\sigma ^2$ and that $X$ is not concentrated in a proper subspace of…

In statistical exercises where there are several candidate models, the traditional approach is to select one model using some data driven criterion and use that model for estimation, testing and other purposes, ignoring the variability of…

We show that bootstrap methods based on the positivity of probability measures provide a systematic framework for studying both synchronous and asynchronous nonequilibrium stochastic processes on infinite lattices. First, we formulate…

This article reviews recent progress in high-dimensional bootstrap. We first review high-dimensional central limit theorems for distributions of sample mean vectors over the rectangles, bootstrap consistency results in high dimensions, and…

Although the operator (spectral) norm is one of the most widely used metrics for covariance estimation, comparatively little is known about the fluctuations of error in this norm. To be specific, let $\hat\Sigma$ denote the sample…

In this paper we study a bootstrap strategy for estimating the variance of a mean taken over large multifactor crossed random effects data sets. We apply bootstrap reweighting independently to the levels of each factor, giving each…

We explore constraints on (1+1)$d$ unitary conformal field theory with an internal $\mathbb{Z}_N$ global symmetry, by bounding the lightest symmetry-preserving scalar primary operator using the modular bootstrap. Among the other constraints…

This paper studies the Gaussian approximation of high-dimensional and non-degenerate U-statistics of order two under the supremum norm. We propose a two-step Gaussian approximation procedure that does not impose structural assumptions on…

We consider the issue of performing accurate small-sample testing inference in beta regression models, which are useful for modeling continuous variates that assume values in $(0,1)$, such as rates and proportions. We derive the Bartlett…

Researchers frequently test and improve model fit by holding a sample constant and varying the model. We propose methods to test and improve sample fit by holding a model constant and varying the sample. Much as the bootstrap is a…

We propose multiplier bootstrap procedures for nonparametric inference and uncertainty quantification of the target mean function, based on a novel framework of integrating target and source data. We begin with the relatively easier…

Bootstrap for nonlinear statistics like U-statistics of dependent data has been studied by several authors. This is typically done by producing a bootstrap version of the sample and plugging it into the statistic. We suggest an alternative…