Related papers: On the Simes inequality and its generalization

Combining several independent measurements of the same physical quantity is one of the most important tasks in metrology. Small samples, biased input estimates, not always adequate reported uncertainties, and unknown error distribution make…

This paper is a companion to our prior paper arXiv:0705.4619 on the `Small Ball Inequality in All Dimensions.' In it, we address a more restrictive inequality, and obtain a non-trivial, explicit bound, using a single essential estimate from…

As a consequence of the Integral Test we find a triple inequality which bounds up and down both a series with respect to its corresponding improper integral, and reciprocally an improper integral with respect to its corresponding series.

Young's inequality is extended to the context of absolutely continuous measures. Several applications are included.

In this note we generalize the trace inequality derived by [1] to the case where the number of terms of the sum (denoted by K) is arbitrary.

In learning-assisted theorem proving, one of the most critical challenges is to generalize to theorems unlike those seen at training time. In this paper, we introduce INT, an INequality Theorem proving benchmark, specifically designed to…

In this paper we present a new approach to proving some exponential inequalities involving the sinc function. Power series expansions are used to generate new polynomial inequalities that are sufficient to prove the given exponential…

There are many different notions of optimality even in testing a single hypothesis. In the multiple testing area, the number of possibilities is very much greater. The paper first will describe multiplicity issues that arise in tests…

The ``impossibility theorem'' -- which is considered foundational in algorithmic fairness literature -- asserts that there must be trade-offs between common notions of fairness and performance when fitting statistical models, except in two…

We consider the problem of hypotheses testing with the basic simple hypothesis: observed sequence of points corresponds to stationary Poisson process with known intensity against a composite one-sided parametric alternative that this is a…

A generalization of Mercer inequality for h-convex function is presented. As application, a weighted generalization of triangle inequality is given.

The goal of this review is to explain some recent results regarding generalizations of the Stein-Tomas (and Strichartz) inequalities to the context of trace ideals (Schatten spaces).

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

Testing of hypotheses is a well studied topic in mathematical statistics. Recently, this issue has also been addressed in the context of Inverse Problems, where the quantity of interest is not directly accessible but only after the…

We provide a new characterization of the logarithmic Sobolev inequality.

The SOM algorithm is very astonishing. On the one hand, it is very simple to write down and to simulate, its practical properties are clear and easy to observe. But, on the other hand, its theoretical properties still remain without proof…

In this article, we focus on the problem of testing the equality of several high dimensional mean vectors with unequal covariance matrices. This is one of the most important problem in multivariate statistical analysis and there have been…

Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies focused on the ways how to express and measure this inconsistency, and several…

This paper proposes a class of origin-smooth approximators of indicators underlying the sum-of-negative-part statistic for testing multiple inequalities. The need for simulation or bootstrap to obtain test critical values is thereby…