Related papers: Asymptotically Minimax Robust Hypothesis Testing
This paper develops a unified framework for asymptotically minimax robust hypothesis testing under distributional uncertainty, applicable to both Bayesian and Neyman--Pearson formulations (Type-I and Type-II). Uncertainty classes based on…
This paper establishes a formal connection between finite-sample and asymptotically minimax robust hypothesis testing under distributional uncertainty. It is shown that, whenever a finite-sample minimax robust test exists, it coincides with…
A robust minimax test for two composite hypotheses, which are determined by the neighborhoods of two nominal distributions with respect to a set of distances - called $\alpha-$divergence distances, is proposed. Sion's minimax theorem is…
The minimax robust hypothesis testing problem for the case where the nominal probability distributions are subject to both modeling errors and outliers is studied in twofold. First, a robust hypothesis testing scheme based on a relative…
This paper provides an overview of results and concepts in minimax robust hypothesis testing for two and multiple hypotheses. It starts with an introduction to the subject, highlighting its connection to other areas of robust statistics and…
We study the robust quickest change detection under unknown pre- and post-change distributions. To deal with uncertainties in the data-generating distributions, we formulate two data-driven ambiguity sets based on the Wasserstein distance,…
The problem of robust hypothesis testing is studied, where under the null and the alternative hypotheses, the data-generating distributions are assumed to be in some uncertainty sets, and the goal is to design a test that performs well…
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…
We present a new framework to address the non-convex robust hypothesis testing problem, wherein the goal is to seek the optimal detector that minimizes the maximum of worst-case type-I and type-II risk functions. The distributional…
Hypothesis testing for small-sample scenarios is a practically important problem. In this paper, we investigate the robust hypothesis testing problem in a data-driven manner, where we seek the worst-case detector over distributional…
The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For…
We study the problem of testing the goodness of fit of categorical count data to a Poisson distribution uniform over the categories, against a class of alternatives defined by excluding an $\ell_p$ ball, $p \leq 2$, of radius $\epsilon$…
In shape-constrained nonparametric inference, it is often necessary to perform preliminary tests to verify whether a probability mass function (p.m.f.) satisfies qualitative constraints such as monotonicity, convexity, or in general…
We study the Neyman-Pearson theory for convex expectations (convex risk measures) on $L^{\infty}(\mu)$. Without assuming that the level sets of penalty functions are weakly compact, a new approach different from the convex duality method is…
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…
This paper considers the design of a minimax test for two hypotheses where the actual probability densities of the observations are located in neighborhoods obtained by placing a bound on the relative entropy between actual and nominal…
Parametric hypothesis testing associated with two independent samples arises frequently in several applications in biology, medical sciences, epidemiology, reliability and many more. In this paper, we propose robust Wald-type tests for…
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,…
We develop a novel computationally efficient and general framework for robust hypothesis testing. The new framework features a new way to construct uncertainty sets under the null and the alternative distributions, which are sets centered…
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…