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A collaborative distributed binary decision problem is considered. Two statisticians are required to declare the correct probability measure of two jointly distributed memoryless process, denoted by $X^n=(X_1,\dots,X_n)$ and…

Information Theory · Computer Science 2016-04-11 Gil Katz , Pablo Piantanida , Merouane Debbah

Consider the problem of binary hypothesis testing. Given $Z$ coming from either $\mathbb P^{\otimes m}$ or $\mathbb Q^{\otimes m}$, to decide between the two with small probability of error it is sufficient, and in many cases necessary, to…

Statistics Theory · Mathematics 2024-03-11 Patrik Róbert Gerber , Yury Polyanskiy

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

This paper considers a problem of distributed hypothesis testing and social learning. Individual nodes in a network receive noisy local (private) observations whose distribution is parameterized by a discrete parameter (hypotheses). The…

Statistics Theory · Mathematics 2016-05-17 Anusha Lalitha , Tara Javidi , Anand Sarwate

We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…

Information Theory · Computer Science 2022-03-30 Jiachun Pan , Yonglong Li , Vincent Y. F. Tan

The hybrid censoring is a mixture of Type I and Type II censoring schemes. This paper presents the statistical inferences of the Inverse Weibull distribution when the data are Type-I hybrid censored. First we consider the maximum likelihood…

Other Statistics · Statistics 2020-04-07 Mohammad Kazemi , Mina Azizpour

In this paper, we revisit the discrete lossy Gray-Wyner problem. In particular, we derive its optimal second-order coding rate region, its error exponent (reliability function) and its moderate deviations constant under mild conditions on…

Information Theory · Computer Science 2017-01-05 Lin Zhou , Vincent Y. F. Tan , Mehul Motani

We study a distributed hypothesis testing setup where peripheral nodes send quantized data to the fusion center in a memoryless fashion. The \emph{expected} number of bits sent by each node under the null hypothesis is kept limited. We…

Information Theory · Computer Science 2022-06-27 Yunus Inan , Mert Kayaalp , Ali H. Sayed , Emre Telatar

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

Power series distributions form a useful subclass of one-parameter discrete exponential families suitable for modeling count data. A zero-inflated power series distribution is a mixture of a power series distribution and a degenerate…

Statistics Theory · Mathematics 2008-12-18 Archan Bhattacharya , Bertrand S. Clarke , Gauri S. Datta

We consider the structural change in a class of discrete valued time series that the conditional distribution follows a one-parameter exponential family. We propose a change-point test based on the maximum likelihood estimator of the…

Statistics Theory · Mathematics 2016-03-01 Mamadou Lamine Diop , William Kengne

We study detection of random signals corrupted by noise that over time switch their values (states) from a finite set of possible values, where the switchings occur at unknown points in time. We model such signals by means of a random…

Information Theory · Computer Science 2017-12-27 Dragana Bajović , Kanghang He , Lina Stanković , Dejan Vukobratović , Vladimir Stanković

We prove that $\tilde{\Theta}(k d^2 / \varepsilon^2)$ samples are necessary and sufficient for learning a mixture of $k$ Gaussians in $\mathbb{R}^d$, up to error $\varepsilon$ in total variation distance. This improves both the known upper…

Machine Learning · Computer Science 2020-07-23 Hassan Ashtiani , Shai Ben-David , Nick Harvey , Christopher Liaw , Abbas Mehrabian , Yaniv Plan

A detection system with a single sensor and $\mathsf{K}$ detectors is considered, where each of the terminals observes a memoryless source sequence and the sensor sends a common message to all the detectors. The communication of this…

Information Theory · Computer Science 2018-05-17 Pierre Escamilla , Michèle Wigger , Abdellatif Zaidi

We study binary hypothesis testing for i.i.d. observations under a multiplicative context weight. For the optimal weighted total loss, defined as the sum of weighted type-I and type-II losses, we prove the logarithmic asymptotic $$ L_n^* =…

Statistics Theory · Mathematics 2026-05-12 Mark Kelbert , El'mira Yu. Kalimulina

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

This paper considers the problem of robust hypothesis testing under non-identically distributed data. We propose Wald-type tests for both simple and composite hypothesis for independent but non-homogeneous observations based on the robust…

Methodology · Statistics 2019-05-09 Ayanendranath Basu , Abhik Ghosh , Nirian Martin , Leandro Pardo

Finite mixtures of multivariate normal distributions have been widely used in empirical applications in diverse fields such as statistical genetics and statistical finance. Testing the number of components in multivariate normal mixture…

Statistics Theory · Mathematics 2019-02-11 Hiroyuki Kasahara , Katsumi Shimotsu

This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…

Numerical Analysis · Mathematics 2025-01-31 Zhiyuan Li , Chunlong Sun , Xiangcheng Zheng

We study the fundamental problems of (i) uniformity testing of a discrete distribution, and (ii) closeness testing between two discrete distributions with bounded $\ell_2$-norm. These problems have been extensively studied in distribution…

Data Structures and Algorithms · Computer Science 2016-11-14 Ilias Diakonikolas , Themis Gouleakis , John Peebles , Eric Price