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This paper develops a flexible distribution-free method for collective outlier detection and enumeration, designed for situations in which the presence of outliers can be detected powerfully even though their precise identification may be…

Methodology · Statistics 2026-05-19 Chiara G. Magnani , Matteo Sesia , Aldo Solari

We consider the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution. This problem is investigated in a sequential setup under mild assumptions on the underlying random process. The…

Signal Processing · Electrical Eng. & Systems 2021-05-07 Dominik Reinhard , Michael Fauß , Abdelhak M. Zoubir

Limit distributions of likelihood ratio statistics are well-known to be discontinuous in the presence of nuisance parameters at the boundary of the parameter space, which lead to size distortions when standard critical values are used for…

Econometrics · Economics 2025-07-29 Giuseppe Cavaliere , Adam McCloskey , Rasmus S. Pedersen , Anders Rahbek

A nonparametric anomalous hypothesis testing problem is investigated, in which there are totally n sequences with s anomalous sequences to be detected. Each typical sequence contains m independent and identically distributed (i.i.d.)…

Machine Learning · Computer Science 2016-12-15 Shaofeng Zou , Yingbin Liang , H. Vincent Poor , Xinghua Shi

In this paper we introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence based (DB) priors. DB priors have simple forms…

Methodology · Statistics 2009-02-27 M. J. Bayarri , G. García-Donato

Sampling algorithms play a pivotal role in probabilistic AI. However, verifying if a sampler program indeed samples from the claimed distribution is a notoriously hard problem. Provably correct testers like Barbarik, Teq, Flash, CubeProbe…

Data Structures and Algorithms · Computer Science 2025-12-09 Rishiraj Bhattacharyya , Sourav Chakraborty , Yash Pote , Uddalok Sarkar , Sayantan Sen

Let $X_1,X_2,...,X_n$ be a sequence of independent or locally dependent random variables taking values in $\mathbb{Z}_+$. In this paper, we derive sharp bounds, via a new probabilistic method, for the total variation distance between the…

Statistics Theory · Mathematics 2010-10-11 Michael V. Boutsikas , Eutichia Vaggelatou

Reproducing Kernel Hilbert Space (RKHS) embedding of probability distributions has proved to be an effective approach, via MMD (maximum mean discrepancy), for nonparametric hypothesis testing problems involving distributions defined over…

Statistics Theory · Mathematics 2025-10-17 Soumya Mukherjee , Bharath K. Sriperumbudur

We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional small diffusions. Our test is based on discrete observation of the processes, and the diffusion coefficient is a nuisance function which…

Statistics Theory · Mathematics 2008-01-29 Ilia Negri , Yoichi Nishiyama

We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…

Statistics Theory · Mathematics 2024-02-14 Aryeh Kontorovich , Amichai Painsky

In this paper, we study change-point testing for high-dimensional linear models, an important problem that has not been well explored in the literature. Specifically, we propose a quadratic-form cumulative sum (CUSUM) statistic to test the…

Statistics Theory · Mathematics 2024-10-23 Zifeng Zhao , Xiaokai Luo , Zongge Liu , Daren Wang

Pearson's chi-squared test, from 1900, is the standard statistical tool for "hypothesis testing on distributions": namely, given samples from an unknown distribution $Q$ that may or may not equal a hypothesis distribution $P$, we want to…

Statistics Theory · Mathematics 2023-10-17 Trung Dang , Walter McKelvie , Paul Valiant , Hongao Wang

A/B testing refers to the task of determining the best option among two alternatives that yield random outcomes. We provide distribution-dependent lower bounds for the performance of A/B testing that improve over the results currently…

Statistics Theory · Mathematics 2015-02-25 Emilie Kaufmann , Olivier Cappé , Aurélien Garivier

Most signal processing and statistical applications heavily rely on specific data distribution models. The Gaussian distributions, although being the most common choice, are inadequate in most real world scenarios as they fail to account…

Statistics Theory · Mathematics 2023-04-17 Ilya Soloveychik

In the "correlated sampling" problem, two players are given probability distributions $P$ and $Q$, respectively, over the same finite set, with access to shared randomness. Without any communication, the two players are each required to…

Computational Complexity · Computer Science 2020-11-24 Mohammad Bavarian , Badih Ghazi , Elad Haramaty , Pritish Kamath , Ronald L. Rivest , Madhu Sudan

We study goodness-of-fit of discrete distributions in the distributed setting, where samples are divided between multiple users who can only release a limited amount of information about their samples due to various information constraints.…

Data Structures and Algorithms · Computer Science 2019-07-23 Jayadev Acharya , Clément L. Canonne , Yanjun Han , Ziteng Sun , Himanshu Tyagi

In this letter, we consider multiple statistical classification problem where a sequence of n independent and identically distributed observations, that are generated by one of M discrete sources, need to be classified. The source…

Information Theory · Computer Science 2021-08-31 Hüseyin Afşer

With model trustworthiness being crucial for sensitive real-world applications, practitioners are putting more and more focus on improving the uncertainty calibration of deep neural networks. Calibration errors are designed to quantify the…

Machine Learning · Computer Science 2024-03-14 Sebastian G. Gruber , Florian Buettner

The paper deals with minimax optimal statistical tests for two composite hypotheses, where each hypothesis is defined by a non-parametric uncertainty set of feasible distributions. It is shown that for every pair of uncertainty sets of the…

Statistics Theory · Mathematics 2018-04-17 Michael Fauss , Abdelhak M. Zoubir , H. Vincent Poor

We resolve a long-standing open question, about the existence of a constant-factor approximation algorithm for the average-case \textsc{Decision Tree} problem with uniform probability distribution over the hypotheses. We answer the question…

Data Structures and Algorithms · Computer Science 2026-04-29 Michał Szyfelbein