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We consider two parametrized random digraph families, namely, proportional-edge and central similarity proximity catch digraphs (PCDs) and compare the performance of these two PCD families in testing spatial point patterns. These PCD…
In applications of group testing in networks, e.g. identifying individuals who are infected by a disease spread over a network, exploiting correlation among network nodes provides fundamental opportunities in reducing the number of tests…
In this paper we introduce a kernel-based measure for detecting differences between two conditional distributions. Using the `kernel trick' and nearest-neighbor graphs, we propose a consistent estimate of this measure which can be computed…
Rao's spacing test is a widely used nonparametric method for assessing uniformity on the circle. However, its broader applicability in practical settings has been limited because the null distribution is not easily calculated. As a result,…
Model-X approaches to testing conditional independence between a predictor and an outcome variable given a vector of covariates usually assume exact knowledge of the conditional distribution of the predictor given the covariates.…
Many relations of scientific interest are nonlinear, and even in linear systems distributions are often non-Gaussian, for example in fMRI BOLD data. A class of search procedures for causal relations in high dimensional data relies on sample…
Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…
We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance correlation vanishes exactly, we are interested in the…
We propose a new method named the Conditional Randomization Rank Test (CRRT) for testing conditional independence of a response variable Y and a covariate variable X, conditional on the rest of the covariates Z. The new method generalizes…
Spherical and hyperspherical data are commonly encountered in diverse applied research domains, underscoring the vital task of assessing independence within such data structures. In this context, we investigate the properties of test…
Testing hypothesis of independence between two random elements on a joint alphabet is a fundamental exercise in statistics. Pearson's chi-squared test is an effective test for such a situation when the contingency table is relatively small.…
Given a symmetric social network, we are interested in testing whether it has only one community or multiple communities. The desired tests should (a) accommodate severe degree heterogeneity, (b) accommodate mixed-memberships, (c) have a…
Testing for independence between graphs is a problem that arises naturally in social network analysis and neuroscience. In this paper, we address independence testing for inhomogeneous Erd\H{o}s-R\'{e}nyi random graphs on the same vertex…
In this article, we consider the problem of testing whether two latent position random graphs are correlated. We propose a test statistic based on the kernel method and introduce the estimation procedure based on the spectral decomposition…
Deciphering the associations between network connectivity and nodal attributes is one of the core problems in network science. The dependency structure and high-dimensionality of networks pose unique challenges to traditional dependency…
Conditional independence tests are crucial across various disciplines in determining the independence of an outcome variable $Y$ from a treatment variable $X$, conditioning on a set of confounders $Z$. The Conditional Randomization Test…
In this paper, we address the problem of testing independence between two high-dimensional random vectors. Our approach involves a series of max-sum tests based on three well-known classes of rank-based correlations. These correlation…
We treat the problem of testing independence between m continuous variables when m can be larger than the available sample size n. We consider three types of test statistics that are constructed as sums or sums of squares of pairwise rank…
We study the fundamental problems of (i) uniformity testing of a discrete distribution, and (ii) closeness testing between two discrete distributions with bounded $\ell_2$-norm. These problems have been extensively studied in distribution…
In this paper, we are concerned with the independence test for $k$ high-dimensional sub-vectors of a normal vector, with fixed positive integer $k$. A natural high-dimensional extension of the classical sample correlation matrix, namely…