Related papers: On Robust Hypothesis Testing with respect to the H…
Many scientific applications involve testing theories that are only partially specified. This task often amounts to testing the goodness-of-fit of a candidate distribution while allowing for reasonable deviations from it. The tolerant…
We consider the problem of estimating the joint distribution $P$ of $n$ independent random variables within the Bayes paradigm from a non-asymptotic point of view. Assuming that $P$ admits some density $s$ with respect to a given reference…
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…
We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters…
We study the problem of testing the covariance matrix of a high-dimensional Gaussian in a robust setting, where the input distribution has been corrupted in Huber's contamination model. Specifically, we are given i.i.d. samples from a…
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…
We consider the hypothesis testing problem of deciding whether an observed high-dimensional vector has independent normal components or, alternatively, if it has a small subset of correlated components. The correlated components may have a…
For the universal hypothesis testing problem, where the goal is to decide between the known null hypothesis distribution and some other unknown distribution, Hoeffding proposed a universal test in the nineteen sixties. Hoeffding's universal…
The problem of robust binary hypothesis testing is studied. Under both hypotheses, the data-generating distributions are assumed to belong to uncertainty sets constructed through moments; in particular, the sets contain distributions whose…
We revisit the distributed hypothesis testing (or hypothesis testing with communication constraints) problem from the viewpoint of privacy. Instead of observing the raw data directly, the transmitter observes a sanitized or randomized…
Health data are often not symmetric to be adequately modeled through the usual normal distributions; most of them exhibit skewed patterns. They can indeed be modeled better through the larger family of skew-normal distributions covering…
We investigate the problem of testing whether a discrete probability distribution over an ordered domain is a histogram on a specified number of bins. One of the most common tools for the succinct approximation of data, $k$-histograms over…
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…
A hypothesis testing algorithm is replicable if, when run on two different samples from the same distribution, it produces the same output with high probability. This notion, defined by by Impagliazzo, Lei, Pitassi, and Sorell [STOC'22],…
Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…
In this letter, we consider multiple statistical classification problem where a sequence of n independent and identically distributed observations, that are generated by one of M discrete sources, need to be classified. The source…
The likelihood ratio statistic, with its asymptotic $\chi^2$ distribution at regular model points, is often used for hypothesis testing. At model singularities and boundaries, however, the asymptotic distribution may not be $\chi^2$, as…
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…
We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…
The most popular hypothesis testing procedure, the likelihood ratio test, is known to be highly non-robust in many real situations. Basu et al. (2013a) provided an alternative robust procedure of hypothesis testing based on the density…