Related papers: The uniformly most powerful test of statistical si…
In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…
An important problem in machine learning and statistics is to identify features that causally affect the outcome. This is often impossible to do from purely observational data, and a natural relaxation is to identify features that are…
In observational studies of discrimination, the most common statistical approaches consider either the rate at which decisions are made (benchmark tests) or the success rate of those decisions (outcome tests). Both tests, however, have…
In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…
We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Specifically, we…
Using the likelihood ratio test statistic, we present a method which can be employed to test the hypothesis of a single Higgs boson using the matrix of measured signal strengths. This method can be applied in the presence of incomplete data…
Hypothesis testing in singular statistical models is often regarded as inherently problematic due to non-identifiability and degeneracy of the Fisher information. We show that the fundamental obstruction to testing in such models is not…
Despite their importance in supporting experimental conclusions, standard statistical tests are often inadequate for research areas, like the life sciences, where the typical sample size is small and the test assumptions difficult to…
A flourishing empirical literature investigates the prevalence of $p$-hacking based on the distribution of $p$-values across studies. Interpreting results in this literature requires a careful understanding of the power of methods for…
Overdispersed count data are modelled with likelihood and non-likelihood approaches. Likelihood approaches include the Poisson mixtures with three distributions, the gamma, the lognormal, and the inverse Gaussian distributions.…
We study the problem of estimating the distribution of effect sizes (the mean of the test statistic under the alternate hypothesis) in a multiple testing setting. Knowing this distribution allows us to calculate the power (type II error) of…
Suppose that at any stage of a statistical experiment a control variable $X$ that affects the distribution of the observed data $Y$ at this stage can be used. The distribution of $Y$ depends on some unknown parameter $\theta$, and we…
The impact of including postcursors in the null hypothesis test is discussed. Unequal prediction probabilities can be included in the null hypothesis test using a generalization of the central limit theorem. A test for determining the…
Consider two random variables contaminated by two unknown transformations. The aim of this paper is to test the equality of those transformations. Two cases are distinguished: first, the two random variables have known distributions.…
In this paper, we consider tests for ultrahigh-dimensional partially linear regression models. The presence of ultrahigh-dimensional nuisance covariates and unknown nuisance function makes the inference problem very challenging. We adopt…
The deviation test belong to core tools in point process statistics, where hypotheses are typically tested considering differences between an empirical summary function and its expectation under the null hypothesis, which depend on a…
It is generally believed that more observations provide more information. However, we observe that in the independence test for rare events, the power of the test is, surprisingly, determined by the number of rare events rather than the…
Computing the state of a quantum mechanical many-body system composed of indistinguishable particles distributed over a multitude of modes is one of the paradigmatic test cases of computational complexity theory: Beyond well-understood…
Particle physics experiments rely on the (generalised) likelihood ratio test (LRT) for searches and measurements, which consist of composite hypothesis tests. However, this test is not guaranteed to be optimal, as the Neyman-Pearson lemma…
We propose a frequentist testing procedure that maintains a defined coverage and is optimal in the sense that it gives maximal power to detect deviations from a null hypothesis when the alternative to the null hypothesis is sampled from a…