Related papers: Variational formulas for the power of the binary h…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
In this paper we introduce a novel procedure for improving multiple testing procedures (MTPs) under scenarios when the null hypothesis $p$-values tend to be stochastically larger than standard uniform (referred to as 'inflated'). An…
In this paper we revisit the binary hypothesis testing problem with one-sided compression. Specifically we assume that the distribution in the null hypothesis is a mixture distribution of iid components. The distribution under the…
It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…
Rule based classifiers that use the presence and absence of key sub-strings to make classification decisions have a natural mechanism for quantifying the uncertainty of their precision. For a binary classifier, the key insight is to treat…
The Jeffreys-Lindley paradox displays how the use of a p-value (or number of standard deviations z) in a frequentist hypothesis test can lead to an inference that is radically different from that of a Bayesian hypothesis test in the form…
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…
In an empirical study of persuasion, researchers often use a binary instrument to encourage individuals to consume information and take some action. We show that, with a binary Imbens-Angrist instrumental variable model and the monotone…
Sample size derivation is a crucial element of the planning phase of any confirmatory trial. A sample size is typically derived based on constraints on the maximal acceptable type I error rate and a minimal desired power. Here, power…
In this paper, we propose an explicit closed-form Bayes factor for the problem of two-sample hypothesis testing. The proposed approach can be regarded as a Bayesian version of the pooled-variance t-statistic and has various appealing…
Multiple testing problems are a staple of modern statistical analysis. The fundamental objective of multiple testing procedures is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to…
We determine the asymptotic behavior of the realized power variations, or more generally of sums of a given test function evaluated at the successive increments of a L\'{e}vy process. One can completely elucidate the first order behavior…
Contemporary testing problems in statistics are increasingly complex, i.e., high-dimensional. Tests based on the $2$- and $\infty$-norm have received considerable attention in such settings, as they are powerful against dense and sparse…
We obtain exact formulas for the cumulative distribution function of the variance-gamma distribution, as infinite series involving the modified Bessel function of the second kind and the modified Lommel function of the first kind. From…
When presenting forensic evidence, such as a DNA match, experts often use the Likelihood ratio (LR) to explain the impact of evidence . The LR measures the probative value of the evidence with respect to a single hypothesis such as 'DNA…
Loss functions serve as the foundation of supervised learning and are often chosen prior to model development. To avoid potentially ad hoc choices of losses, statistical decision theory describes a desirable property for losses known as…
We revisit the problem of asymmetric binary hypothesis testing against a composite alternative hypothesis. We introduce a general framework to treat such problems when the alternative hypothesis adheres to certain axioms. In this case we…
Statistical techniques are used in all branches of science to determine the feasibility of quantitative hypotheses. One of the most basic applications of statistical techniques in comparative analysis is the test of equality of two…
The statistical analysis of discrete data has been the subject of extensive statistical research dating back to the work of Pearson. In this survey we review some recently developed methods for testing hypotheses about high-dimensional…
Upper bounds are given for the weight distribution of binary weakly self-dual codes. To get these new bounds, we introduce a novel method of utilizing unitary operations on Hilbert spaces. This method is motivated by recent progress on…