Related papers: The Case for Raabe's Test

We propose a new approach to sequential testing which is an adaptive (on-line) extension of the (off-line) framework developed in [10]. It relies upon testing of pairs of hypotheses in the case where each hypothesis states that the vector…

The well-known Leibniz theorem (Leibniz Criterion or alternating series test) of convergence of alternating series is generalized for the case when the absolute value of terms of series are "not absolutely monotonously" convergent to zero.…

This paper describes an algorithm for determining radii of convergence of power expansions for algebraic functions and the testing done to check it. Since the current methods for computing these series are iterative, standard methods for…

Statistical hypothesis testing, as formalized by 20th Century statisticians and taught in college statistics courses, has been a cornerstone of 100 years of scientific progress. Nevertheless, the methodology is increasingly questioned in…

Bayesian evidence ratios give a very attractive way of comparing models, and being able to quote the odds on a particular model seems a very clear motivation for making a choice. Jeffreys' scale of evidence is often used in the…

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.

Testing the equality of two proportions is a common procedure in science, especially in medicine and public health. In these domains it is crucial to be able to quantify evidence for the absence of a treatment effect. Bayesian hypothesis…

We consider the Reeb graph of a thickening of points sampled from an unknown space. Our main contribution is a framework to transfer reconstruction results similar to the well-known work of Niyogi, Smale, and Weinberger to the setting of…

We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. For such random dynamical systems, we consider estimates of absolutely continuous…

This paper develops a Bayesian approach for assessing equivalence and non-inferiority hypotheses in two-arm trials using relative belief ratios. A relative belief ratio is a measure of statistical evidence and can indicate evidence either…

In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…

Likelihood ratio tests are intuitively appealing. Nevertheless, a number of examples are known in which they perform very poorly. The present paper discusses a large class of situations in which this is the case, and analyzes just how…

In large scale genetic association studies, a primary aim is to test for association between genetic variants and a disease outcome. The variants of interest are often rare, and appear with low frequency among subjects. In this situation,…

The familiar second derivative test for convexity, combined with resolvent calculus, is shown to yield a useful tool for the study of convex matrix-valued functions. We demonstrate the applicability of this approach on a number of theorems…

Kleene algebra with tests is an extension of Kleene algebra, the algebra of regular expressions, which can be used to reason about programs. We develop a coalgebraic theory of Kleene algebra with tests, along the lines of the coalgebraic…

In many situations it could be interesting to ascertain whether nonparametric regression curves can be grouped, especially when confronted with a considerable number of curves. The proposed testing procedure allows to determine groups with…

In this paper, we revisit the task of negation resolution, which includes the subtasks of cue detection (e.g. "not", "never") and scope resolution. In the context of previous shared tasks, a variety of evaluation metrics have been proposed.…

We provide a novel tool which may be used to construct new examples of positive maps in matrix algebras (or, equivalently, entanglement witnesses). It turns out that this can be used to prove positivity of several well known maps (such as…

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

In this paper, we develop a simple approach for testing multiple statistical hypotheses based on the observations of a number of probability ratios enumerated consecutively with respect to the index of hypotheses. Explicit and tight bounds…