Related papers: Strong approximations of level exceedences related…
An important aspect of multiple hypothesis testing is controlling the significance level, or the level of Type I error. When the test statistics are not independent it can be particularly challenging to deal with this problem, without…
Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample…
This paper studies distributed binary test of statistical independence under communication (information bits) constraints. While testing independence is very relevant in various applications, distributed independence test is particularly…
Many tools exist to detect dependence between random variables, a core question across a wide range of machine learning, statistical, and scientific endeavors. Although several statistical tests guarantee eventual detection of any…
Independence testing is a fundamental problem in statistical inference: given samples from a joint distribution $p$ over multiple random variables, the goal is to determine whether $p$ is a product distribution or is $\epsilon$-far from all…
The maximum type-I and type-II error exponents associated with the newly introduced almost-fixed-length hypothesis testing is characterized. In this class of tests, the decision-maker declares the true hypothesis almost always after…
We show that the control of the false discovery rate (FDR) for a multiple testing procedure is implied by two coupled simple sufficient conditions. The first one, which we call ``self-consistency condition'', concerns the algorithm itself,…
Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…
It is quite common in modern research, for a researcher to test many hypotheses. The statistical (frequentist) hypothesis testing framework, does not scale with the number of hypotheses in the sense that naively performing many hypothesis…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…
In this article, we consider the problem of testing the independence between two random variables. Our primary objective is to develop tests that are highly effective at detecting associations arising from explicit or implicit functional…
Statistical dependence between hypotheses poses a significant challenge to the stability of large scale multiple hypotheses testing. Ignoring it often results in an unacceptably large spread in the false positive proportion even though the…
Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…
In this paper, we have established a general framework of multistage hypothesis tests which applies to arbitrarily many mutually exclusive and exhaustive composite hypotheses. Within the new framework, we have constructed specific…
Bell inequalities or Bell-like experiments are supposed to test hidden variable theories based on three intuitive assumptions: determinism, locality and measurement independence. If one of the assumptions of Bell inequality is properly…
Correlated observations are ubiquitous phenomena in a plethora of scientific avenues. Tackling this dependence among test statistics has been one of the pertinent problems in simultaneous inference. However, very little literature exists…
It is frequently of interest to jointly analyze two paired sequences of multiple tests. This paper studies the problem of detecting whether there are more pairs of tests that are significant in both sequences than would be expected by…
We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance correlation vanishes exactly, we are interested in the…
In this paper we propose several variants to perform the independence test between two random elements based on recurrence rates. We will show how to calculate the test statistic in each one of these cases. From simulations we obtain that…
In this article, we consider the problem of simultaneous testing of hypotheses when the individual test statistics are not necessarily independent. Specifically, we consider the problem of simultaneous testing of point null hypotheses…