Related papers: Conditional Independence Testing for Discrete Dist…
We consider the problem of conditional independence testing of $X$ and $Y$ given $Z$ where $X,Y$ and $Z$ are three real random variables and $Z$ is continuous. We focus on two main cases - when $X$ and $Y$ are both discrete, and when $X$…
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…
The categorical Gini correlation proposed by Dang et al. is a dependence measure to characterize independence between categorical and numerical variables. The asymptotic distributions of the sample correlation under dependence and…
Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper…
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…
In this paper, our interest is in the problem of simultaneous hypothesis testing when the test statistics corresponding to the individual hypotheses are possibly correlated. Specifically, we consider the case when the test statistics…
We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are non-nested and their intersection is a union of two marginal independences. We consider two sequences of such…
This paper investigates the utilization of maximum and average distance correlations for multivariate independence testing. We characterize their consistency properties in high-dimensional settings with respect to the number of marginally…
Competing risks data with discrete lifetime comes up in practice. However, only limited literature exists for such data. In this paper, we propose a non-parametric test based on U-statistics for testing independence of time to failure and…
Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the…
Conditional independence testing (CIT) is a common task in machine learning, e.g., for variable selection, and a main component of constraint-based causal discovery. While most current CIT approaches assume that all variables are numerical…
This paper proposes new parametric model adequacy tests for possibly nonlinear and nonstationary time series models with noncontinuous data distribution, which is often the case in applied work. In particular, we consider the correct…
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…
Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly…
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…
Testing two potentially multivariate variables for statistical dependence on the basis finite samples is a fundamental statistical challenge. Here we explore a family of tests that adapt to the complexity of the relationship between the…
Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample…
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…
We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete or mixture of those, with light tails or heavy…
A new computationally efficient dependence measure, and an adaptive statistical test of independence, are proposed. The dependence measure is the difference between analytic embeddings of the joint distribution and the product of the…