Related papers: Optimal Statistical Hypothesis Testing for Social …
We derive uniformly most powerful (UMP) tests for simple and one-sided hypotheses for a population proportion within the framework of Differential Privacy (DP), optimizing finite sample performance. We show that in general, DP hypothesis…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
We consider the problem of deciding on sampling strategy, in particular sampling design. We propose a risk measure, whose minimizing value guides the choice. The method makes use of a superpopulation model and takes into account uncertainty…
We investigate the problem of jointly testing a pair of composite hypotheses and, depending on the test result, estimating a random parameter under distributional uncertainties. Specifically, it is assumed that the distribution of the data…
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…
We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…
A new method based on the rejection sampling for finding statistical tests is proposed. This method is conceptually intuitive, easy to implement, and applicable for arbitrary dimension. To illustrate its potential applicability, three…
This paper studies optimal hypothesis testing for nonregular econometric models with parameter-dependent support. We consider both one-sided and two-sided hypothesis testing and develop asymptotically uniformly most powerful tests based on…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
Uniformly most powerful tests are statistical hypothesis tests that provide the greatest power against a fixed null hypothesis among all tests of a given size. In this article, the notion of uniformly most powerful tests is extended to the…
Selective classification enhances the reliability of predictive models by allowing them to abstain from making uncertain predictions. In this work, we revisit the design of optimal selection functions through the lens of the Neyman--Pearson…
This paper addresses the issues of conservativeness and computational complexity of probabilistic robustness analysis. We solve both issues by defining a new sampling strategy and robustness measure. The new measure is shown to be much less…
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…
In this paper, after a discussion of general properties of statistical tests, we present the construction of the most powerful hypothesis test for determining the existence of a new phenomenon in counting-type experiments where the observed…
This paper studies Markov Decision Processes under parameter uncertainty. We adapt the distributionally robust optimization framework, and assume that the uncertain parameters are random variables following an unknown distribution, and…
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 consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
We propose and study a general method for construction of consistent statistical tests on the basis of possibly indirect, corrupted, or partially available observations. The class of tests devised in the paper contains Neyman's smooth…
The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…
Multiple testing problems are a staple of modern statistical analysis. The fundamental objective of multiple testing procedures is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to…