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The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…

Statistics Theory · Mathematics 2022-11-15 Loris Michel , Jeffrey Näf , Nicolai Meinshausen

In this paper, we propose novel, fully Bayesian non-parametric tests for one-sample and two-sample multivariate location problems. We model the underlying distribution using a Dirichlet process prior, and develop a testing procedure based…

Statistics Theory · Mathematics 2021-08-03 Indrabati Bhattacharya , Subhashis Ghosal

We study Martin-L\"{o}f random (ML-random) points on computable probability measures on sample and parameter spaces (Bayes models). We consider variants of conditional randomness defined by ML-randomness on Bayes models and those of…

Information Theory · Computer Science 2023-04-24 Hayato Takahashi

In this paper, we revisit the classical problem of solving over-determined systems of nonsmooth equations numerically. We suggest a nonsmooth Levenberg--Marquardt method for its solution which, in contrast to the existing literature, does…

Optimization and Control · Mathematics 2023-11-10 Lateef O. Jolaoso , Patrick Mehlitz , Alain B. Zemkoho

Empirical phi-divergence test-statistics have demostrated to be a useful technique for the simple null hypothesis to improve the finite sample behaviour of the classical likelihood ratio test-statistic, as well asfor model misspecification…

Methodology · Statistics 2016-01-15 Narayanaswamy Balakrishnan , Nirian Martin , Leandro Pardo

We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we…

Statistics Theory · Mathematics 2017-07-03 Sivaraman Balakrishnan , Larry Wasserman

When the competing classes in a classification problem are not of comparable size, many popular classifiers exhibit a bias towards larger classes, and the nearest neighbor classifier is no exception. To take care of this problem, we develop…

Methodology · Statistics 2023-11-02 Anvit Garg , Anil K. Ghosh , Soham Sarkar

The maximum likelihood degree of a statistical model refers to the number of solutions, where the derivative of the log-likelihood function is zero, over the complex field. This paper examines the maximum likelihood degree of the parameter…

Statistics Theory · Mathematics 2025-02-10 Pooja Yadav , Tanuja Srivastava

We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights, i.e., optimal multiple stopping, for a robust evaluation that accounts for model…

The behavior of maximum likelihood estimates (MLEs) and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied. This class of problems differs radically from the…

Statistics Theory · Mathematics 2009-09-29 Moulinath Banerjee

This note discusses the problem of choosing between hypotheses in a situation with many, correlated non-normal variables. A new method is introduced to shrink the many variables into a smaller subset of variables with zero mean, unit…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Byron P. Roe

A number of discrete time, finite population size models in genetics describing the dynamics of allele frequencies are known to converge (subject to suitable scaling) to a diffusion process in the infinite population limit, termed the…

Probability · Mathematics 2021-09-14 Jaromir Sant , Paul A. Jenkins , Jere Koskela , Dario Spano

Inference based on the penalized density ratio model is proposed and studied. The model under consideration is specified by assuming that the log--likelihood function of two unknown densities is of some parametric form. The model has been…

Statistics Theory · Mathematics 2008-07-17 Konstantinos Fokianos

We investigate the problem of multiclass classification with rejection, where a classifier can choose not to make a prediction to avoid critical misclassification. First, we consider an approach based on simultaneous training of a…

Machine Learning · Statistics 2019-10-31 Chenri Ni , Nontawat Charoenphakdee , Junya Honda , Masashi Sugiyama

This study develops a framework for testing hypotheses on structural parameters in incomplete models. Such models make set-valued predictions and hence do not generally yield a unique likelihood function. The model structure, however,…

Econometrics · Economics 2019-12-03 Hiroaki Kaido , Yi Zhang

While there appears to be a general consensus in the literature on the definition of the estimand and estimator associated with the Wilcoxon-Mann-Whitney test, it seems somewhat less clear as to how best to estimate the variance. In…

Methodology · Statistics 2022-08-03 Claus P. Nowak , Markus Pauly , Edgar Brunner

A model of Poissonian observation having a jump (change-point) in the intensity function is considered. Two cases are studied. The first one corresponds to the situation when the jump size converges to a non-zero limit, while in the second…

Statistics Theory · Mathematics 2015-02-25 Serguei Dachian , Lin Yang

For general data, the number of complex solutions to the likelihood equations is constant and this number is called the (maximum likelihood) ML-degree of the model. In this article, we describe the special locus of data for which the…

Algebraic Geometry · Mathematics 2015-10-01 Emil Horobet , Jose Israel Rodriguez

The von Mises-Fisher distribution is one of the most widely used probability distributions to describe directional data. Finite mixtures of von Mises-Fisher distributions have found numerous applications. However, the likelihood function…

Methodology · Statistics 2022-03-08 Tin Lok James Ng

The two-sample homogeneity testing problem is fundamental in statistics and becomes particularly challenging in high dimensions, where classical tests can suffer substantial power loss. We develop a learning-assisted procedure based on the…

Methodology · Statistics 2026-01-30 Xiaoyu Hu , Zhenhua Lin