Related papers: Hypothesis testing under uniform-block covariance …
Evaluating blocked randomized experiments from a potential outcomes perspective has two primary branches of work. The first focuses on larger blocks, with multiple treatment and control units in each block. The second focuses on matched…
While statistical learning methods have proved powerful tools for predictive modeling, the black-box nature of the models they produce can severely limit their interpretability and the ability to conduct formal inference. However, the…
Voxel-based analysis methods localize brain structural differences by performing voxel-wise statistical comparisons on two groups of images aligned to a common space. This procedure requires highly accurate registration as well as a…
We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the…
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…
Distributed frameworks are widely used to handle massive data, where sample size $n$ is very large, and data are often stored in $k$ different machines. For a random vector $X\in \mathbb{R}^p$ with expectation $\mu$, testing the mean vector…
While covariance matrices have been widely studied in many scientific fields, relatively limited progress has been made on estimating conditional covariances that permits a large covariance matrix to vary with high-dimensional subject-level…
Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required…
Multivariate hypergeometric distribution arises frequently in elementary statistics and probability courses, for simultaneously studying the occurence law of specified events, when sampling without replacement from a finite population with…
We consider infinite-dimensional Hilbert space-valued random variables that are assumed to be temporal dependent in a broad sense. We prove a central limit theorem for the moving block bootstrap and for the tapered block bootstrap, and show…
We establish a profound connection between coherent risk measures, a prominent object in quantitative finance, and uniform integrability, a fundamental concept in probability theory. Instead of working with absolute values of random…
Modern high-throughput biomedical devices routinely produce data on a large scale, and the analysis of high-dimensional datasets has become commonplace in biomedical studies. However, given thousands or tens of thousands of measured…
The presence of outlying observations may adversely affect statistical testing procedures that result in unstable test statistics and unreliable inferences depending on the distortion in parameter estimates. In spite of the fact that the…
Unimodality constitutes a key property indicating grouping behavior of the data around a single mode of its density. We propose a method that partitions univariate data into unimodal subsets through recursive splitting around valley points…
We consider the problem of uncertainty assessment for low dimensional components in high dimensional models. Specifically, we propose a decorrelated score function to handle the impact of high dimensional nuisance parameters. We consider…
Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the…
One of the classic concerns in statistics is determining if two samples come from thesame population, i.e. homogeneity testing. In this paper, we propose a homogeneitytest in the context of Functional Data Analysis, adopting an idea from…
Accurately specifying covariance structures is critical for valid inference in longitudinal and functional data analysis, particularly when data are sparsely observed. In this study, we develop a global goodness-of-fit test to assess…
Block maxima methods constitute a fundamental part of the statistical toolbox in extreme value analysis. However, most of the corresponding theory is derived under the simplifying assumption that block maxima are independent observations…
To conduct a more in-depth investigation of randomized solvers for solving linear systems, we adopt a unified randomized batch-sampling Kaczmarz framework with per-iteration costs as low as cyclic block methods, and develop a general…