Related papers: Second-level randomness test based on the Kolmogor…
Given two networks of differing sizes, it is of interest to test whether the two networks belong to the same distribution. We formalize the notion of "equality of distribution" under the framework of the generalized random dot product…
Hypothesis testing is a central problem in statistical analysis, and there is currently a lack of differentially private tests which are both statistically valid and powerful. In this paper, we develop several new differentially private…
Given independent samples from P and Q, two-sample permutation tests allow one to construct exact level tests when the null hypothesis is P=Q. On the other hand, when comparing or testing particular parameters $\theta$ of P and Q, such as…
How can one determine whether a community-level treatment, such as the introduction of a social program or trade shock, alters agents' incentives to form links in a network? This paper proposes analogues of a two-sample Kolmogorov-Smirnov…
We propose a new goodness-of-fit test for copulas, based on empirical copula processes and their nonparametric bootstrap counterparts. The standard Kolmogorov-Smirnov type test for copulas that takes the supremum of the empirical copula…
Testing hypotheses of goodness-of-fit about mixture distributions on the basis of independent but not necessarily identically distributed random vectors is considered. The hypotheses are given by a specific distribution or by a family of…
Goodness-of-fit tests gauge whether a given set of observations is consistent (up to expected random fluctuations) with arising as independent and identically distributed (i.i.d.) draws from a user-specified probability distribution known…
In this article, we introduce the novel concept of the second maximum of a Gaussian random field on a Riemannian submanifold. This second maximum serves as a powerful tool for characterizing the distribution of the maximum. By utilizing an…
We interpret likelihood-based test functions from a geometric perspective where the Kullback-Leibler (KL) divergence is adopted to quantify the distance from a distribution to another. Such a test function can be seen as a sub-Gaussian…
This paper proposes confidence regions for the identified set in conditional moment inequality models using Kolmogorov-Smirnov statistics with a truncated inverse variance weighting with increasing truncation points. The new weighting…
We propose novel kernel-based tests for assessing the equivalence between distributions. Traditional goodness-of-fit testing is inappropriate for concluding the absence of distributional differences, because failure to reject the null…
Non-degenerate U-empirical Kolmogorov-Smirnov tests are studied and their large deviation asymptotics under the null-hypothesis is described. Several examples of such statistics used for testing goodness-of-fit and symmetry are considered.…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
We propose a sequential nonparametric test for detecting a change in distribution, based on windowed Kolmogorov--Smirnov statistics. The approach is simple, robust, highly computationally efficient, easy to calibrate, and requires no…
Big Data has become an ever more commonplace setting that is encountered by data analysts. In the Big Data setting, analysts are faced with very large numbers of observations as well as data that arrive as a stream, both of which are…
We consider the problem of testing the equality of conditional distributions of a response variable given a vector of covariates between two populations. Such a hypothesis testing problem can be motivated from various machine learning and…
We establish inequalities that compare the p-Wasserstein distance to distances which are built as suprema of box measures. More precisely, when the measures are supported on $[0,1]^d$, we obtain sharp upper-bounds of the $p$-Wasserstein…
We consider a binary statistical hypothesis testing problem, where $n$ independent and identically distributed random variables $Z^n$ are either distributed according to the null hypothesis $P$ or the alternate hypothesis $Q$, and only $P$…
We construct new testing procedures for spherical and elliptical symmetry based on the characterization that a random vector $X$ with finite mean has a spherical distribution if and only if $\Ex[u^\top X | v^\top X] = 0$ holds for any two…
We propose here a new goodness-of-fit test, named the one-sample OVL-q test (q = 1, 2, . . .), which can be considered an extension of the one-sample Kolmogorov-Smirnov test (equivalent to the one-sample OVL-1 test). We have analyzed the…