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It is well-known that in some situations it is not easy to compute the likelihood function as the datasets might be large or the model is too complex. In that contexts composite likelihood, derived by multiplying the likelihoods of subjects…
Graph-based tests are a class of non-parametric two-sample tests useful for analyzing high-dimensional data. The test statistics are constructed from similarity graphs (such as K-minimum spanning tree), and consequently, their performance…
The likelihood ratio test is widely used in exploratory factor analysis to assess the model fit and determine the number of latent factors. Despite its popularity and clear statistical rationale, researchers have found that when the…
A frequent problem in statistical science is how to properly handle missing data in matched paired observations. There is a large body of literature coping with the univariate case. Yet, the ongoing technological progress in measuring…
Using the fact that some depth functions characterize certain family of distribution functions, and under some mild conditions, distribution of the depth is continuous, we have constructed several new multivariate goodness of fit tests…
Pearson's chi-square tests are among the most commonly applied statistical tools across a wide range of scientific disciplines, including medicine, engineering, biology, sociology, marketing and business. However, its usage in some areas is…
The small sample universal hypothesis testing problem is investigated in this paper, in which the number of samples $n$ is smaller than the number of possible outcomes $m$. The goal of this work is to find an appropriate criterion to…
Consider a random sample of $n$ independently and identically distributed $p$-dimensional normal random vectors. A test statistic for complete independence of high-dimensional normal distributions, proposed by Schott (2005), is defined as…
In this paper, we provide a statistical testing framework to check whether a random sample splitting in a multi-dimensional space is carried out in a valid way, which could be directly applied to A/B testing and multivariate testing to…
We consider the problem of detecting a general sparse mixture and obtain an explicit characterization of the phase transition under some conditions, generalizing the univariate results of Cai and Wu. Additionally, we provide a sufficient…
The recently developed "Data Set Diagonalization" method (DSD) is applied to measure compatibility of the data sets that are used to determine parton distribution functions (PDFs). Discrepancies among the experiments are found to be…
Two-sample tests for multivariate data and especially for non-Euclidean data are not well explored. This paper presents a novel test statistic based on a similarity graph constructed on the pooled observations from the two samples. It can…
It is well-known that each statistic in the family of power divergence statistics, across $n$ trials and $r$ classifications with index parameter $\lambda\in\mathbb{R}$ (the Pearson, likelihood ratio and Freeman-Tukey statistics correspond…
Hypothesis testing in high dimensional data is a notoriously difficult problem without direct access to competing models' likelihood functions. This paper argues that statistical divergences can be used to quantify the difference between…
A multivariate distribution function F is in the max-domain of attraction of an extreme value distribution if and only if this is true for the copula corresponding to F and its univariate margins. Aulbach et al. (2012a) have shown that a…
Comparing $K$-sample distributions is a fundamental problem in data science that arises in a wide variety of fields and applications. In this article, we introduce a maximum-of-differences approach to make such comparisons. Specifically, we…
Testing the equality in distributions of multiple samples is a common task in many fields. However, this problem for high-dimensional or non-Euclidean data has not been well explored. In this paper, we propose new nonparametric tests based…
Pearson's Chi-squared test, though widely used for detecting association between categorical variables, exhibits low statistical power in large sparse contingency tables. To address this limitation, two novel permutation tests have been…
Graph matching is the process of computing the similarity between two graphs. Depending on the requirement, it can be exact or inexact. Exact graph matching requires a strict correspondence between nodes of two graphs, whereas inexact…
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…