Related papers: Statistical tests for whether a given set of indep…
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…
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…
We examine the extent to which sublinear-sample property testing and estimation apply to settings where samples are independently but not identically distributed. Specifically, we consider the following distributional property testing…
Motivated by a problem in population genetics, we examine the combinatorics of dissimilarity for pairs of random unordered draws of multiple objects, with replacement, from a collection of distinct objects. Consider two draws of size $K$…
One of the most fundamental problems in distribution testing is the identity testing problem: given samples $x_1,\ldots,x_s$, the goal is to determine whether the samples are drawn from a target distribution $\mathcal{D}$. When…
We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from $s$ distributions, $p_1, p_2, \ldots, p_s$, we design testers for the…
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 study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…
Consider $n$ iid random variables, where $\xi_1, \ldots, \xi_n$ are $n$ realisations of a random variable $\xi$ and $\zeta_1, \ldots, \zeta_n$ are $n$ realisations of a random variable $\zeta$. The distribution of each realisation of $\xi$,…
We analyzed the effect of the deviation of the exact distribution of the p-values from the uniform distribution on the Kolmogorov-Smirnov (K-S) test that was implemented as the second-level randomness test. We derived an inequality that…
In this work, we study non-parametric hypothesis testing problem with distribution function constraints. The empirical likelihood ratio test has been widely used in testing problems with moment (in)equality constraints. However, some…
Based on cumulative distribution functions, Fourier series expansion and Kolmogorov tests, we present a simple method to display probability densities for data drawn from a continuous distribution. It is often more efficient than using…
We consider a system of weak* closed sets of finite-dimensional distributions. We show that a corresponding system of random variables can be defined on a probability space with a probability measure determined up to some set of measures,…
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…
Experiments often yield non-identically distributed data for statistical analysis. Tests of hypothesis under such set-ups are generally performed using the likelihood ratio test, which is non-robust with respect to outliers and model…
We propose a simple way of testing whether a given set of observations can come from a given theoretical cumulative distribution. In the test more weight is attached to the tails of the distribution than in the usual Kolmogorov or Smirnov…
When comparing two distributions, it is often helpful to learn at which quantiles or values there is a statistically significant difference. This provides more information than the binary "reject" or "do not reject" decision of a global…
Let $G$ be a large (simple, unlabeled) dense graph on $n$ vertices. Suppose that we only know, or can estimate, the empirical distribution of the number of subgraphs $F$ that each vertex in $G$ participates in, for some fixed small graph…
We propose a simple and intuitive test for arguably the most prevailing hypothesis in statistics that data are independent and identically distributed (IID), based on a newly introduced off-diagonal sequential U-process. This IID test is…
The two-sample Kolmogorov-Smirnov test is a widely used statistical test for detecting whether two samples are likely to come from the same distribution. Implementations typically recur on an article of Hodges from 1957. The advances in…