Related papers: independence: Fast Rank Tests
Let $(Y,(X_i)_{i\in\mathcal{I}})$ be a zero mean Gaussian vector and $V$ be a subset of $\mathcal{I}$. Suppose we are given $n$ i.i.d. replications of the vector $(Y,X)$. We propose a new test for testing that $Y$ is independent of…
Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…
We consider settings in which the data of interest correspond to pairs of ordered times, e.g, the birth times of the first and second child, the times at which a new user creates an account and makes the first purchase on a website, and the…
We consider the problem of non-parametric Conditional Independence testing (CI testing) for continuous random variables. Given i.i.d samples from the joint distribution $f(x,y,z)$ of continuous random vectors $X,Y$ and $Z,$ we determine…
Since the two seminal papers by Fisher (1915, 1921) were published, the test under a fixed value correlation coefficient null hypothesis for the bivariate normal distribution constitutes an important statistical problem. In the framework of…
A new index based on empirical copulas, termed the Copula Statistic (CoS), is introduced for assessing the strength of multivariate dependence and for testing statistical independence. New properties of the copulas are proved. They allow us…
Independence screening is a variable selection method that uses a ranking criterion to select significant variables, particularly for statistical models with nonpolynomial dimensionality or "large p, small n" paradigms when p can be as…
Independence testing is a classical statistical problem that has been extensively studied in the batch setting when one fixes the sample size before collecting data. However, practitioners often prefer procedures that adapt to the…
Deep learning methods have proved highly effective for classification and image recognition problems. In this paper, we ask whether this success can be transferred to hypothesis testing: if a neural network can distinguish, for example, an…
The multiscale Fisher's independence test (MULTIFIT hereafter) proposed by Gorsky & Ma (2022) is a novel method to test independence between two random vectors. By its design, this test is particularly useful in detecting local dependence.…
In this paper, we characterize several classes of continuous radial basis functions that can be employed to determine whether a interaction of a probability is zero or not. These functions encompass standard independence tests but also the…
The purpose of this paper is twofold. First, we provide a novel characterization of independence of random vectors based on the checkerboard approximation to a multivariate copula. Using this result, we then propose a new family of tests of…
Sampling algorithms play a pivotal role in probabilistic AI. However, verifying if a sampler program indeed samples from the claimed distribution is a notoriously hard problem. Provably correct testers like Barbarik, Teq, Flash, CubeProbe…
This work addresses testing the independence of two continuous and finite-dimensional random variables from the design of a data-driven partition. The empirical log-likelihood statistic is adopted to approximate the sufficient statistics of…
We show that the stochastic independence of real-valued random variables is equivalent to the conditional uncorrelation, where the conditioning takes place over the Cartesian products of intervals. Next, we express the mutual independence…
In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…
We describe a family of conservative statistical tests for independence of two autocorrelated time series. The series may take values in any sets, and one of them must be stationary. A user-specified function quantifying the association of…
We define generalized innovations associated with generalized error models having arbitrary distributions, that is, distributions that can be mixtures of continuous and discrete distributions. These models include stochastic volatility…
This paper introduces an innovative method for conducting conditional independence testing in high-dimensional data, facilitating the automated discovery of significant associations within distinct subgroups of a population, all while…
Multivariate time series data that capture the temporal evolution of interconnected systems are ubiquitous in diverse areas. Understanding the complex relationships and potential dependencies among co-observed variables is crucial for the…