English
Related papers

Related papers: Optimal sequential tests yield log-optimal e-proce…

200 papers

This work analyzes the asymptotic performances of fully distributed sequential hypothesis testing procedures as the type-I and type-II error rates approach zero, in the context of a sensor network without a fusion center. In particular, the…

Applications · Statistics 2018-04-17 Shang Li , Xiaodong Wang

We study the sequential empirical process indexed by general function classes and its smoothed set-indexed analogue. Sufficient conditions for asymptotic equicontinuity are provided for nonstationary arrays of time series. This yields…

Probability · Mathematics 2025-08-19 Florian Alexander Scholze , Ansgar Steland

E-values and E-processes (nonnegative supermartingales) provide anytime-valid evidence for sequential testing via Ville's inequality, yet their connection to Bayesian reasoning, representational structure, and computational feasibility are…

Statistics Theory · Mathematics 2026-03-11 Nicholas G. Polson , Vadim Sokolov , Daniel Zantedeschi

We propose a new approach to sequential testing which is an adaptive (on-line) extension of the (off-line) framework developed in [10]. It relies upon testing of pairs of hypotheses in the case where each hypothesis states that the vector…

Statistics Theory · Mathematics 2017-02-27 Anatoli Juditsky , Arkadi Nemirovski

Consider $K$ processes, each generating a sequence of identical and independent random variables. The probability measures of these processes have random parameters that must be estimated. Specifically, they share a parameter $\theta$…

Machine Learning · Computer Science 2022-10-12 Arpan Mukherjee , Ali Tajer , Pin-Yu Chen , Payel Das

This article demonstrates how recent developments in the theory of empirical processes allow us to construct a new family of asymptotically distribution-free smooth tests. Their distribution-free property is preserved even when the…

Statistics Theory · Mathematics 2026-02-24 Xiangyu Zhang , Sara Algeri

Three-stage $t$-tests of separated one-sided hypotheses are derived, extending Lorden's optimal three-stage tests for the one-dimensional exponential family by using Lai and Zhang's generalization of Schwarz's optimal fully-sequential tests…

Statistics Theory · Mathematics 2007-06-13 Jay Bartroff

We consider the problem of quickly detecting a signal in a sensor network when the subset of sensors in which signal may be present is completely unknown. We formulate this problem as a sequential hypothesis testing problem with a simple…

Statistics Theory · Mathematics 2013-11-12 Georgios Fellouris , Alexander Tartakovsky

We review some developments on clustering stochastic processes and come with the conclusion that asymptotically consistent clustering algorithms can be obtained when the processes are ergodic and the dissimilarity measure satisfies the…

Machine Learning · Statistics 2019-08-07 Qidi Peng , Nan Rao , Ran Zhao

We design sequential tests for a large class of nonparametric null hypotheses based on elicitable and identifiable functionals. Such functionals are defined in terms of scoring functions and identification functions, which are ideal…

Statistics Theory · Mathematics 2023-06-06 Philippe Casgrain , Martin Larsson , Johanna Ziegel

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 consider the construction of optimal tests of equivalence hypotheses. Specifically, assume X_1,..., X_n are i.i.d. with distribution P_{\theta}, with \theta \in R^k. Let g(\theta) be some real-valued parameter of interest.…

Statistics Theory · Mathematics 2007-06-13 Joseph P. Romano

We consider a quantum system that is being continuously monitored, giving rise to a measurement signal. From such a stream of data, information needs to be inferred about the underlying system's dynamics. Here we focus on hypothesis testing…

Quantum Physics · Physics 2024-03-27 Giulio Gasbarri , Matias Bilkis , Elisabet Roda-Salichs , John Calsamiglia

Sequential monitoring of randomized trials traditionally relies on parametric assumptions or asymptotic approximations. We discuss a family of nonparametric sequential tests - collectively called e-RT - for binary, event-only, and…

Methodology · Statistics 2026-05-12 Fernando G Zampieri

Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses…

Statistics Theory · Mathematics 2020-10-26 Michael Fauss , Abdelhak M. Zoubir , H. Vincent Poor

We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular our goal is to discriminate between two arbitrary quantum states with a prescribed error…

This article develops a method to construct the optimal sequential test for monitoring the changes in the distribution of finite observation sequences with a general dependence structure. This method allows us to prove that different…

Statistics Theory · Mathematics 2019-08-01 Dong Han , Fugee Tsung , Jinguo Xian

In this paper, we present a novel method for computing the asymptotic values of both the optimal threshold, and the probability of success in sequences of optimal stopping problems. This method, based on the resolution of a first-order…

Probability · Mathematics 2022-05-18 L. Bayón , P. Fortuny , J. M. Grau , A. M. Oller-Marcén , M. M. Ruiz

Adaptive clinical trials rely on interim analyses, flexible stopping, and data-dependent design modifications that complicate statistical guarantees when fixed-horizon test statistics are repeatedly inspected or reused after adaptations.…

Methodology · Statistics 2026-02-09 Alexandra Sokolova , Vadim Sokolov

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