Related papers: Moderate Deviations Analysis of Binary Hypothesis …
We study the binary hypothesis testing problem where an adversary may potentially corrupt a fraction of the samples. The detector is, however, permitted to abstain from making a decision if (and only if) the adversary is present. We…
We provide a general approach to obtain upper bounds for small deviations $ \mathbb{P}(\Vert y \Vert \le \epsilon)$ in different norms, namely the supremum and $\beta$- H\"older norms. The large class of processes $y$ under consideration…
We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with…
Softmax distributions are widely used in machine learning, including Large Language Models (LLMs), where the attention unit uses softmax distributions. We abstract the attention unit as the softmax model, where given a vector input, the…
The aim of this article is to make a contribution to the Bayesian procedure of testing precise hypotheses for parametric models. For this purpose, we define the Bayesian Discrepancy Measure that allows one to evaluate the suitability of a…
In this paper, two new classes of lower bounds on the probability of error for $m$-ary hypothesis testing are proposed. Computation of the minimum probability of error which is attained by the maximum a-posteriori probability (MAP)…
This note investigates a number of scenarios in which unadjusted testing following a blinded sample size re-estimation leads to type I error violations. For superiority testing, this occurs in certain small-sample borderline cases. We…
You measure the value of a quantity x for a number of systems (cells, molecules, people, chunks of metal, DNA vectors, etc.). You repeat the whole set of measures in different occasions or assays, which you try to design as equal to one…
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…
We establish a Cram\'er-type moderate deviation theorem for double-index permutation statistics (DIPS). To the best of our knowledge, previous results only provided Berry-Esseen type bounds for DIPS, which cannot yield moderate deviation…
Various statistical tests have been developed for testing the equality of means in matched pairs with missing values. However, most existing methods are commonly based on certain distributional assumptions such as normality, 0-symmetry or…
We consider a novel paradigm for Bayesian testing of hypotheses and Bayesian model comparison. Our alternative to the traditional construction of posterior probabilities that a given hypothesis is true or that the data originates from a…
This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error…
We propose new concentration inequalities for self-normalized martingales. The main idea is to introduce a suitable weighted sum of the predictable quadratic variation and the total quadratic variation of the martingale. It offers much more…
We provide non-asymptotic, relative deviation bounds for the eigenvalues of empirical covariance and Gram matrices in general settings. Unlike typical uniform bounds, which may fail to capture the behavior of smaller eigenvalues, our…
We study how to perform tests on samples of pairs of observations and predictions in order to assess whether or not the predictions are prudent. Prudence requires that that the mean of the difference of the observation-prediction pairs can…
This article gives a synopsis on new developments in affine invariant tests for multivariate normality in an i.i.d.-setting, with special emphasis on asymptotic properties of several classes of weighted $L^2$-statistics. Since weighted…
Heavy-tailed errors impair the accuracy of the least squares estimate, which can be spoiled by a single grossly outlying observation. As argued in the seminal work of Peter Huber in 1973 [{\it Ann. Statist.} {\bf 1} (1973) 799--821], robust…
Mean-deviation models, along with the existing theory of coherent risk measures, are well studied in the literature. In this paper, we characterize monotonic mean-deviation (risk) measures from a general mean-deviation model by applying a…
The research described in this paper is motivated by model checking for parametric single-index models with diverging number of predictors. To construct a test statistic, we first study the asymptotic property of the estimators of involved…