Related papers: Asymptotically Minimax Robust Hypothesis Testing
We consider the problem of sequentially testing a simple null hypothesis versus a composite alternative hypothesis that consists of a finite set of densities. We study sequential tests that are based on thresholding of mixture-based…
Lack-of-fit testing of a regression model with Berkson measurement error has not been discussed in the literature to date. To fill this void, we propose a class of tests based on minimized integrated square distances between a nonparametric…
We consider inference on the first principal direction of a $p$-variate elliptical distribution. We do so in challenging double asymptotic scenarios for which this direction eventually fails to be identifiable. In order to achieve…
Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…
Minimax optimization problems are an important class of optimization problems arising from both modern machine learning and from traditional research areas. We focus on the stability of constrained minimax optimization problems based on the…
Consider a binary statistical hypothesis testing problem, where $n$ independent and identically distributed random variables $Z^n$ are either distributed according to the null hypothesis $P$ or the alternative hypothesis $Q$, and only $P$…
We study the problem of closeness testing for continuous distributions and its implications for causal discovery. Specifically, we analyze the sample complexity of distinguishing whether two multidimensional continuous distributions are…
In hypothesis testing, the phenomenon of label noise, in which hypothesis labels are switched at random, contaminates the likelihood functions. In this paper, we develop a new method to determine the decision rule when we do not have…
We analyze hypotheses tests using classical results on large deviations to compare two models, each one described by a different H\"older Gibbs probability measure. One main difference to the classical hypothesis tests in Decision Theory is…
Minimum divergence methods are popular tools in a variety of statistical applications. We consider tubular model adequacy tests, and demonstrate that the new divergences that are generated in the process are very useful in robust…
Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical techniques based on maximum likelihood and related methods. Recently Ghosh et al. (2013) proposed a general class…
We consider the problem of hypothesis testing in the situation when the first hypothesis is simple and the second one is local one-sided composite. We describe the choice of the thresholds and the power functions of the Score Function test,…
We study asymptotic properties of Bayesian multiple testing procedures and provide sufficient conditions for strong consistency under general dependence structure. We also consider a novel Bayesian multiple testing procedure and associated…
In any parametric inference problem, the robustness of the procedure is a real concern. A procedure which retains a high degree of efficiency under the model and simultaneously provides stable inference under data contamination is…
Ever since the proof of asymptotic normality of maximum likelihood estimator by Cramer (1946), it has been understood that a basic technique of the Taylor series expansion suffices for asymptotics of $M$-estimators with…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
The density band model proposed by Kassam for robust hypothesis testing is revisited in this paper. First, a novel criterion for the general characterization of least favorable distributions is proposed, which unifies existing results. This…
The popular criteria of optimality for quickest change detection procedures are the Lorden criterion, the Shiryaev-Roberts-Pollak criterion, and the Bayesian criterion. In this paper a robust version of these quickest change detection…
We show that the tensor product of two random linear codes is robustly testable with high probability. This implies that one can obtain pairs of linear codes such that their product and the product of their dual codes are simultaneously…
Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical maximum likelihood based techniques. Recently Ghosh et al. (2013) proposed a general class of divergence measures…