Related papers: Power one sequential tests exist for weakly compac…
The practice of pooling several individual test statistics to form aggregate tests is common in many statistical application where individual tests may be underpowered. While selection by aggregate tests can serve to increase power, the…
We introduce a notion of real-valued reward testing for probabilistic processes by extending the traditional nonnegative-reward testing with negative rewards. In this richer testing framework, the may and must preorders turn out to be…
Low energy antiprotons offer excellent opportunities to study properties of fundamental forces and symmetries in nature. Experiments with them can contribute substantially to deepen our fundamental knowledge in atomic, nuclear and particle…
We show that, under suitably general formulations, covering properties, accumulation properties and filter convergence are all equivalent notions. This general correspondence is exemplified in the study of products. Let $X$ be a product of…
We revisit the fundamental question of simple-versus-simple hypothesis testing with an eye towards computational complexity, as the statistically optimal likelihood ratio test is often computationally intractable in high-dimensional…
There is a rich theory of existence theorems for minimizers over reflexive Sobolev spaces (ex. Eberlein-\v{S}mulian theorem). However, the existence theorems for many variational problems over non-reflexive Sobolev spaces remain…
This paper addresses the following general scenario: A scientist wishes to perform a battery of experiments, each generating a sequential stream of data, to investigate some phenomenon. The scientist would like to control the overall error…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
This paper considers the problem of robust hypothesis testing under non-identically distributed data. We propose Wald-type tests for both simple and composite hypothesis for independent but non-homogeneous observations based on the robust…
Cauchy combination test has been widely used for combining correlated p-values, but it may fail to work under certain scenarios. We propose a truncated Cauchy combination test (TCCT) which focus on combining p-values with arbitrary…
Given two sets of independent samples from unknown distributions $P$ and $Q$, a two-sample test decides whether to reject the null hypothesis that $P=Q$. Recent attention has focused on kernel two-sample tests as the test statistics are…
We consider inference on the first principal direction of a $p$-variate elliptical distribution. We do so in challenging double asymptotic scenarios for which this direction eventually fails to be identifiable. In order to achieve…
This paper places conformal testing in a general framework of statistical hypothesis testing. A standard approach to testing a composite null hypothesis $H$ is to test each of its elements and to reject $H$ when each of its elements is…
Replicability is central to scientific progress, and the partial conjunction (PC) hypothesis testing framework provides an objective tool to quantify it across disciplines. Existing PC methods assume independent studies. Yet many modern…
In this paper we study the modulus of continuity of weak solutions to a singular elliptic equation in the plane under very weak assumption on the integrability of the elliptic coefficients. Our investigation reveals that the modulus of…
We propose a new powerful family of tests of univariate normality. These tests are based on an initial value problem in the space of characteristic functions originating from the fixed point property of the normal distribution in the zero…
Many testing problems are readily amenable to randomised tests such as those employing data splitting. However despite their usefulness in principle, randomised tests have obvious drawbacks. Firstly, two analyses of the same dataset may…
The aim of this paper is to determine the logical and computational strength of instances of the Bolzano-Weierstra{\ss} principle (BW) and a weak variant of it. We show that BW is instance-wise equivalent to the weak K\"onig's lemma for…
We study the sequential testing problem of two alternative hypotheses regarding an unknown parameter in an exponential family when observations are costly. In a Bayesian setting, the problem can be embedded in a Markovian framework. Using…
Local versions of measurability have been around for a long time. Roughly, one splits the notion of $\mu $-completeness into pieces, and asks for a uniform ultrafilter over $\mu $ satisfying just some piece of $\mu $-completeness. Analogue…