Related papers: Pure Significance Tests for Multinomial and Binomi…
The probability integral transform (PIT) of a continuous random variable $X$ with distribution function $F_X$ is a uniformly distributed random variable $U=F_X(X)$. We define the angular probability integral transform (APIT) as $\theta_U =…
Efficient verification of multipartite quantum states is crucial to many applications in quantum information processing. By virtue of Schmidt decomposition and mutually unbiased bases, here we propose a universal protocol to verify…
This paper considers the problem of testing the equality of two unspecified distributions. The classical omnibus tests such as the Kolmogorov-Smirnov and Cram\`er-von Mises are known to suffer from low power against essentially all but…
Statistical significance testing is widely accepted as a means to assess how well a difference in effectiveness reflects an actual difference between systems, as opposed to random noise because of the selection of topics. According to…
In modern data analysis, statistical efficiency improvement is expected via effective collaboration among multiple data holders with non-shared data. In this article, we propose a collaborative score-type test (CST) for testing linear…
In this work, we consider the sample complexity required for testing the monotonicity of distributions over partial orders. A distribution $p$ over a poset is monotone if, for any pair of domain elements $x$ and $y$ such that $x \preceq y$,…
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…
Motivated by the question of data quantization and "binning," we revisit the problem of identity testing of discrete probability distributions. Identity testing (a.k.a. one-sample testing), a fundamental and by now well-understood problem…
We develop here several goodness-of-fit tests for testing the k-monotonicity of a discrete density, based on the empirical distribution of the observations. Our tests are non-parametric, easy to implement and are proved to be asymptotically…
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…
In some applications, an experimental unit is composed of two distinct but related subunits. The response from such a unit is $(X_{1}, X_{2})$ but we observe only $Y_1 = \min\{X_{1},X_{2}\}$ and $Y_2 = \max\{X_{1},X_{2}\}$, i.e., the…
The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…
Exact null distributions of goodness-of-fit test statistics are generally challenging to obtain in tractable forms. Practitioners are therefore usually obliged to rely on asymptotic null distributions or Monte Carlo methods, either in the…
Selective inference is a subfield of statistics that enables valid inference after selection of a data-dependent question. In this paper, we introduce selectively dominant p-values, a class of p-values that allow practitioners to easily…
This study presents a new procedure for necessary tests of multivariate normality based on the uniform distribution on the Stiefel manifold. We demonstrate that the test statistic, which is formed by the product of the scaled residual…
We describe a simple test of the spatial uniformity of an ensemble of discrete events. Given an estimate for the point source luminosity function and an instrumental point spread function (PSF), a robust upper bound on the fractional point…
Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…
Large-scale multiple testing problems require the simultaneous assessment of many p-values. This paper compares several methods to assess the evidence in multiple binomial counts of p-values: the maximum of the binomial counts after…
The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability…
In this paper we propose a computationally efficient multiple hypothesis testing procedure for persistent homology. The computational efficiency of our procedure is based on the observation that one can empirically simulate a null…