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This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is…

Statistics Theory · Mathematics 2009-12-23 Andrey Novikov

In this paper we explore the behaviour of dependent test statistics for testing of multiple hypothesis . To keep simplicity, we have considered a mixture normal model with equicorrelated correlation set up. With a simple linear…

Statistics Theory · Mathematics 2020-01-09 Rahul Roy , Subir Kumar Bhandari

Sequential likelihood ratio testing is found to be most powerful in sequential studies with early stopping rules when grouped data come from the one-parameter exponential family. First, to obtain this elusive result, the probability measure…

Methodology · Statistics 2021-01-28 Sergey Tarima , Nancy Flournoy

In this paper, we introduce a flexible and widely applicable nonparametric entropy-based testing procedure that can be used to assess the validity of simple hypotheses about a specific parametric population distribution. The testing…

Econometrics · Economics 2022-01-19 Ron Mittelhammer , George Judge , Miguel Henry

We propose three test criteria each of which is appropriate for testing, respectively, the equivalence hypotheses of symmetry, of homogeneity, and of independence, with multivariate data. All quantities have the common feature of involving…

Methodology · Statistics 2023-11-09 Feifei Chen , Simos G. Meintanis , Lixing Zhu

Given observations from a circular random variable contaminated by an additive measurement error, we consider the problem of minimax optimal goodness-of-fit testing in a non-asymptotic framework. We propose direct and indirect testing…

Statistics Theory · Mathematics 2020-07-14 Sandra Schluttenhofer , Jan Johannes

Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…

Information Theory · Computer Science 2018-12-07 Lin Zhou , Vincent Y. F. Tan , Mehul Motani

This paper is concerned with testing normality in a Hilbert space based on the maximum mean discrepancy. Specifically, we discuss the behavior of the test from two standpoints: asymptotics and practical aspects. Asymptotic normality of the…

Statistics Theory · Mathematics 2019-02-12 Natsumi Makigusa , Kanta Naito

In group sequential designs, where several data looks are conducted for early stopping, we generally assume the vector of test statistics from the sequential analyses follows (at least approximately or asymptotially) a multivariate normal…

Statistics Theory · Mathematics 2024-04-22 Long-Hao Xu , Tobias Mütze , Frank Konietschke , Tim Friede

Given a random sample of observations, mixtures of normal densities are often used to estimate the unknown continuous distribution from which the data come. Here we propose the use of this semiparametric framework for testing symmetry about…

Methodology · Statistics 2012-04-23 Silvia Bacci , Francesco Bartolucci

Let $X_1,X_2,...$ be a discrete-time stochastic process with a distribution $P_\theta$, $\theta\in\Theta$, where $\Theta$ is an open subset of the real line. We consider the problem of testing a simple hypothesis $H_0:$ $\theta=\theta_0$…

Statistics Theory · Mathematics 2009-12-23 Andrey Novikov , Petr Novikov

We revisit the fundamental question of simple-versus-simple hypothesis testing with an eye towards computational complexity, as the statistically optimal likelihood ratio test is often computationally intractable in high-dimensional…

Statistics Theory · Mathematics 2025-05-05 Ankur Moitra , Alexander S. Wein

It has been recently shown that e-processes are sufficient for sequential testing in the following sense: every level-$\alpha$ sequential test can be obtained by thresholding an e-process at $1/\alpha$. However, in the above result, neither…

Statistics Theory · Mathematics 2026-05-14 Ashwin Ram , Aaditya Ramdas

We study a variant of quantum hypothesis testing wherein an additional 'inconclusive' measurement outcome is added, allowing one to abstain from attempting to discriminate the hypotheses. The error probabilities are then conditioned on a…

Quantum Physics · Physics 2024-07-09 Bartosz Regula , Ludovico Lami , Mark M. Wilde

We propose a new class of goodness-of-fit tests for the inverse Gaussian distribution. The proposed tests are weighted $L^2$-type tests depending on a tuning parameter. We develop the asymptotic theory under the null hypothesis and under a…

Methodology · Statistics 2022-01-31 J. S. Allison , S. Betsch , B. Ebner , I. J. H. Visagie

We consider goodness-of-fit tests with i.i.d. samples generated from a categorical distribution $(p_1,...,p_k)$. For a given $(q_1,...,q_k)$, we test the null hypothesis whether $p_j=q_{\pi(j)}$ for some label permutation $\pi$. The…

Statistics Theory · Mathematics 2018-07-30 Chao Gao

We study the adversarial binary hypothesis testing problem in the sequential setting. Associated with each hypothesis is a closed, convex set of distributions. Given the hypothesis, each observation is generated according to a distribution…

Information Theory · Computer Science 2025-11-14 Eeshan Modak , Mayank Bakshi , Bikash Kumar Dey , Vinod M. Prabhakaran

We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…

Data Structures and Algorithms · Computer Science 2020-09-15 Ilias Diakonikolas , Themis Gouleakis , Daniel M. Kane , John Peebles , Eric Price

We propose an e-value based framework for testing arbitrary composite nulls against composite alternatives, when an $\epsilon$ fraction of the data can be arbitrarily corrupted. Our tests are inherently sequential, being valid at arbitrary…

Methodology · Statistics 2025-12-25 Aytijhya Saha , Aaditya Ramdas

The object of study is the problem of testing for uniformity of the multinomial distribution. We consider tests based on symmetric statistics, defined as the sum of some function of cell-frequencies. Mainly, attention is focused on the…

Statistics Theory · Mathematics 2022-09-12 Sherzod M. Mirakhmedov