Related papers: A complete characterization of testable hypotheses
A new measure of non-classical correlations is introduced and characterized. It tests the ability of using a state {\rho} of a composite system AB as a probe for a quantum illumination task [e.g. see S. Lloyd, Science 321, 1463 (2008)], in…
Data-driven most powerful tests are statistical hypothesis decision-making tools that deliver the greatest power against a fixed null hypothesis among all corresponding data-based tests of a given size. When the underlying data…
We provide a characterization in terms of Fatou closedness for weakly closed monotone convex sets in the space of $\mathcal{P}$-quasisure bounded random variables, where $\mathcal{P}$ is a (possibly non-dominated) class of probability…
We investigate the connection between measure, capacity and algorithmic randomness for the space of closed sets. For any computable measure m, a computable capacity T may be defined by letting T(Q) be the measure of the family of closed…
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,…
A common problem in genetics is that of testing whether a set of highly dependent gene expressions differ between two populations, typically in a high-dimensional setting where the data dimension is larger than the sample size. Most…
We investigate the power of weak measurements in the framework of quantum state discrimination. First, we define and analyze the notion of weak consecutive measurements. Our main result is a convergence theorem whereby we demonstrate when…
The validity of classical hypothesis testing requires the significance level $\alpha$ be fixed before any statistical analysis takes place. This is a stringent requirement. For instance, it prohibits updating $\alpha$ during (or after) an…
In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…
Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current…
We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ points from an arbitrary probability measure in $\mathbf{R}^d$ relates to the wet part of that measure. This extends classical results for…
Ratios of universal enumerable semimeasures corresponding to hypotheses are investigated as a solution for statistical composite hypotheses testing if an unbounded amount of computation time can be assumed. Influence testing for discrete…
In this note we look at the interdependences between James' theorem and the boundary problem. To do so we show a variant of James' sup-theorem for C(K)-spaces conjectured by Godefroy: in order to know that a bounded weakly closed subset of…
A test of the null hypothesis that a hazard rate is monotone nondecreasing, versus the alternative that it is not, is proposed. Both the test statistic and the means of calibrating it are new. Unlike previous approaches, neither is based on…
The theory of generalised measurements is used to examine the problem of discriminating unambiguously between non-orthogonal pure quantum states. Measurements of this type never give erroneous results, although, in general, there will be a…
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…
This paper presents a new variation of Tverberg's theorem. Given a discrete set $S$ of $R^d$, we study the number of points of $S$ needed to guarantee the existence of an $m$-partition of the points such that the intersection of the $m$…
Testing for independence between two random vectors is a fundamental problem in statistics. It is observed from empirical studies that many existing omnibus consistent tests may not work well for some strongly nonmonotonic and nonlinear…
We prove in a direct fashion that a multidimensional probability measure is determinate if the higher dimensional analogue of Carleman's condition is satisfied. In that case, the polynomials, as well as certain proper subspaces of the…
Scoring rules measure the deviation between a probabilistic forecast and reality. Strictly proper scoring rules have the property that for any forecast, the mathematical expectation of the score of a forecast p by the lights of p is…