Related papers: Studentized Tests of Independence: Random-Lifter a…
Observations of suspected coherent elastic neutrino-nucleus scatterings by dark matter direct detection experiments highlight the need for an investigation into the so-called "neutrino floor". We focus on the discovery limit, a statistical…
The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…
We revisit resampling procedures for error estimation in binary classification in terms of U-statistics. In particular, we exploit the fact that the error rate estimator involving all learning-testing splits is a U-statistic. Thus, it has…
Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
We develop a novel computationally efficient and general framework for robust hypothesis testing. The new framework features a new way to construct uncertainty sets under the null and the alternative distributions, which are sets centered…
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…
Many real-world bandit applications are characterized by sparse rewards, which can significantly hinder learning efficiency. Leveraging problem-specific structures for careful distribution modeling is recognized as essential for improving…
We present some product representations for random variables with the Linnik, Mittag-Leffler and Weibull distributions and establish the relationship between the mixing distributions in these representations. Based on these representations,…
Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…
Motivated by the stochastic block model, we investigate a class of Wigner-type matrices with certain block structures, and establish a CLT for the corresponding linear spectral statistics via the large-deviation bounds from local law and…
We introduce an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic and study its…
Given independent samples generated from the joint distribution $p(\mathbf{x},\mathbf{y},\mathbf{z})$, we study the problem of Conditional Independence (CI-Testing), i.e., whether the joint equals the CI distribution…
We consider the problem of inference in shift-share research designs. The choice between existing approaches that allow for unrestricted spatial correlation involves tradeoffs, varying in terms of their validity when there are relatively…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…
We consider a two-sample hypothesis testing problem, where the distributions are defined on the space of undirected graphs, and one has access to only one observation from each model. A motivating example for this problem is comparing the…
The question of testing for equality in distribution between two linear models, each consisting of sums of distinct discrete independent random variables with unequal numbers of observations, has emerged from the biological research. In…
We consider a class of elliptic random matrices which generalize two classical ensembles from random matrix theory: Wigner matrices and random matrices with iid entries. In particular, we establish a central limit theorem for linear…
We present a novel approach to estimating discrete distributions with (potentially) infinite support in the total variation metric. In a departure from the established paradigm, we make no structural assumptions whatsoever on the sampling…
Non-deterministic measurements are common in real-world scenarios: the performance of a stochastic optimization algorithm or the total reward of a reinforcement learning agent in a chaotic environment are just two examples in which…