Related papers: Gap-Measure Tests with Applications to Data Integr…
We investigate a generalized empirical likelihood approach in a two-group setting where the constraints on parameters have a form of U-statistics. In this situation, the summands that consist of the constraints for the empirical likelihood…
Many experiments can be interpreted in terms of random processes operating according to some internal protocols. When experiments are costly or cannot be repeated only one or a few finite samples are available. In this paper we study data…
Pearson's chi-squared test is widely used to assess the uniformity of discrete histograms, typically relying on a continuous chi-squared distribution to approximate the test statistic, since computing the exact distribution is…
In this paper, we consider methods for performing hypothesis tests on data protected by a statistical disclosure control technology known as differential privacy. Previous approaches to differentially private hypothesis testing either…
The question of testing for equality in distribution between two linear models, each consisting of sums of distinct discrete independent random variables with unequal numbers of observations, has emerged from the biological research. In…
We study the problem of generalized uniformity testing \cite{BC17} of a discrete probability distribution: Given samples from a probability distribution $p$ over an {\em unknown} discrete domain $\mathbf{\Omega}$, we want to distinguish,…
We present the $U$-Statistic Permutation (USP) test of independence in the context of discrete data displayed in a contingency table. Either Pearson's chi-squared test of independence, or the $G$-test, are typically used for this task, but…
Weighted histograms are used for the estimation of probability density functions. Computer simulation is the main domain of application of this type of histogram. A review of chi-square goodness of fit tests for weighted histograms is…
Statistical depth, which measures the center-outward rank of a given sample with respect to its underlying distribution, has become a popular and powerful tool in nonparametric inference. In this paper, we investigate the use of statistical…
This paper introduces a quasi-likelihood ratio testing procedure for diffusion processes observed under nonsynchronous sampling schemes. High-frequency data, particularly in financial econometrics, are often recorded at irregular time…
We study the problem of testing the goodness of fit of categorical count data to a Poisson distribution uniform over the categories, against a class of alternatives defined by excluding an $\ell_p$ ball, $p \leq 2$, of radius $\epsilon$…
Maximum likelihood fits to data can be performed using binned data and unbinned data. The likelihood fits in either case produce only the fitted quantities but not the goodness of fit. With binned data, one can obtain a measure of the…
Distribution testing can be described as follows: $q$ samples are being drawn from some unknown distribution $P$ over a known domain $[n]$. After the sampling process, a decision must be made about whether $P$ holds some property, or is far…
If a discrete probability distribution in a model being tested for goodness-of-fit is not close to uniform, then forming the Pearson chi-square statistic can involve division by nearly zero. This often leads to serious trouble in practice…
We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the…
Goodness-of-fit tests based on the Euclidean distance often outperform chi-square and other classical tests (including the standard exact tests) by at least an order of magnitude when the model being tested for goodness-of-fit is a discrete…
In this paper, we investigate sphericity testing in high-dimensional settings, where existing methods primarily rely on sum-type test procedures that often underperform under sparse alternatives. To address this limitation, we propose two…
In this paper, we develop new test statistics for private hypothesis testing. These statistics are designed specifically so that their asymptotic distributions, after accounting for noise added for privacy concerns, match the asymptotics of…
Two modifications of the chi square test for comparing usual(unweighted) and weighted histograms and two weighted histograms are proposed. Numerical examples illustrate an application of the tests for the histograms with different…
A massive dataset often consists of a growing number of (potentially) heterogeneous sub-populations. This paper is concerned about testing various forms of heterogeneity arising from massive data. In a general nonparametric framework, a set…