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This study focuses on an alignment-free sequence comparison method: the number of words of length k shared between two sequences, also known as the D_2 statistic. The advantages of the use of this statistic over alignment-based methods are…
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…
High-dimensional linear regression has been thoroughly studied in the context of independent and identically distributed data. We propose to investigate high-dimensional regression models for independent but non-identically distributed…
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 class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test…
An important class of two-sample multivariate homogeneity tests is based on identifying differences between the distributions of interpoint distances. While generating distances from point clouds offers a straightforward and intuitive way…
Random intersection graphs have received much attention recently and been used in a wide range of applications ranging from key predistribution in wireless sensor networks to modeling social networks. For these graphs, each node is equipped…
A number of biomedical problems require performing many hypothesis tests, with an attendant need to apply stringent thresholds. Often the data take the form of a series of predictor vectors, each of which must be compared with a single…
Tukey's $g$-and-$h$ distribution has been a powerful tool for data exploration and modeling since its introduction. However, two long standing challenges associated with this distribution family have remained unsolved until this day: how to…
The rapid development of modern technology facilitates the appearance of numerous unprecedented complex data which do not satisfy the axioms of Euclidean geometry, while most of the statistical hypothesis tests are available in Euclidean or…
Testing mutual independence among multiple random variables is a fundamental problem in statistics, with wide applications in genomics, finance, and neuroscience. In this paper, we propose a new class of tests for high-dimensional mutual…
Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…
We propose a valid and consistent test for the hypothesis that two latent distance random graphs on the same vertex set have the same generating latent positions, up to some unidentifiable similarity transformations. Our test statistic is…
The use of data-random graphs in statistical testing of spatial patterns is introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the points from various classes.…
A number of applications require two-sample testing on ranked preference data. For instance, in crowdsourcing, there is a long-standing question of whether pairwise comparison data provided by people is distributed similar to…
Inference based on the penalized density ratio model is proposed and studied. The model under consideration is specified by assuming that the log--likelihood function of two unknown densities is of some parametric form. The model has been…
A popular approach for testing if two univariate random variables are statistically independent consists of partitioning the sample space into bins, and evaluating a test statistic on the binned data. The partition size matters, and the…
We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over…
High-dimensional feature selection is a central problem in a variety of application domains such as machine learning, image analysis, and genomics. In this paper, we propose graph-based tests as a useful basis for feature selection. We…
Testing differences between a treatment and control group is common practice in biomedical research like randomized controlled trials (RCT). The standard two-sample t-test relies on null hypothesis significance testing (NHST) via p-values,…