Related papers: Power one sequential tests exist for weakly compac…
We consider the problem of designing optimal level-$\alpha$ power-one tests for composite nulls. Given a parameter $\alpha \in (0,1)$ and a stream of $\mathcal{X}$-valued observations $\{X_n: n \geq 1\} \overset{i.i.d.}{\sim} P$, the goal…
Let $X_1,X_2,...$ be a discrete-time stochastic process with a distribution $P_\theta$, $\theta\in\Theta$, where $\Theta$ is an open subset of the real line. We consider the problem of testing a simple hypothesis $H_0:$ $\theta=\theta_0$…
A Partial Conjunction Hypothesis (PCH) test combines information across a set of base hypotheses to determine whether some subset is non-null. PCH tests arise in a diverse array of fields, but standard PCH testing methods can be highly…
We prove two lower bounds for stopping times of sequential tests between general composite nulls and alternatives. The first lower bound is for the setting where the type-1 error level $\alpha$ approaches zero, and equals $\log(1/\alpha)$…
We consider the problem of sequentially testing a simple null hypothesis versus a composite alternative hypothesis that consists of a finite set of densities. We study sequential tests that are based on thresholding of mixture-based…
We develop e-values and e-processes testing the null hypothesis that a distribution over nonnegative integers is monotone, and that a distribution over integers is unimodal given a certain mode. Our e-processes lead to tests of power one…
We consider the problem of constructing sequential power-one tests where the null and alternative classes are specified indirectly through historical or offline data. More specifically, given an offline dataset consisting of observations…
We introduce a simple tool to control for false discoveries and identify individual signals in scenarios involving many tests, dependent test statistics, and potentially sparse signals. The tool applies the Cauchy combination test…
How can we monitor, in real time, whether one uncertain prospect has any upside over another? To answer this question, we develop a novel family of sequential, anytime-valid tests for stochastic dominance (SD; also known as stochastic…
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…
Let $X_1,X_2,..., X_n,...$ be a stochastic process with independent values whose distribution $P_\theta$ depends on an unknown parameter $\theta$, $\theta\in\Theta$, where $\Theta$ is an open subset of the real line. The problem of testing…
Robust tests of general composite hypothesis under non-identically distributed observations is always a challenge. Ghosh and Basu (2018, Statistica Sinica, 28, 1133--1155) have proposed a new class of test statistics for such problems based…
$P$-values that are derived from continuously distributed test statistics are typically uniformly distributed on $(0,1)$ under least favorable parameter configurations (LFCs) in the null hypothesis. Conservativeness of a $p$-value $P$…
In this paper, we derive power guarantees of some sequential tests for bounded mean under general alternatives. We focus on testing procedures using nonnegative supermartingales which are anytime valid and consider alternatives which…
We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…
Sequential likelihood ratio testing is found to be most powerful in sequential studies with early stopping rules when grouped data come from the one-parameter exponential family. First, to obtain this elusive result, the probability measure…
Power series distributions form a useful subclass of one-parameter discrete exponential families suitable for modeling count data. A zero-inflated power series distribution is a mixture of a power series distribution and a degenerate…
On observing a sequence of i.i.d.\ data with distribution $P$ on $\mathbb{R}^d$, we ask the question of how one can test the null hypothesis that $P$ has a log-concave density. This paper proves one interesting negative and positive result:…
In the binary hypothesis testing problem, it is well known that sequentiality in taking samples eradicates the trade-off between two error exponents, yet implementing the optimal test requires the knowledge of the underlying distributions,…
We consider the problem of hypothesis testing in the situation where the first hypothesis is simple and the second one is local one-sided composite. We describe the choice of the thresholds and the power functions of different tests when…