Related papers: Graphical tests of independence for general distri…
Recognizing, quantifying and visualizing associations between two variables is increasingly important. This paper investigates how a new function-valued measure of dependence, the quantile dependence function, can be used to construct tests…
Graphical models have long been studied in statistics as a tool for inferring conditional independence relationships among a large set of random variables. The most existing works in graphical modeling focus on the cases that the data are…
Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data…
In the classical two-sample problem, the conventional approach for testing distributions equality is based on the difference between the two marginal empirical distribution functions, whereas a test for independence is based on the contrast…
Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These tests, however, can be unreliable, and algorithms are sensitive to…
Conditional independence and graphical models are well studied for probability distributions on product spaces. We propose a new notion of conditional independence for any measure $\Lambda$ on the punctured Euclidean space $\mathbb…
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…
We suggest a dependence coefficient between a categorical variable and some general variable taking values in a metric space. We derive important theoretical properties and study the large sample behaviour of our suggested estimator.…
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 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…
In this paper we propose several variants to perform the independence test between two random elements based on recurrence rates. We will show how to calculate the test statistic in each one of these cases. From simulations we obtain that…
Despite major methodological developments, Bayesian inference for Gaussian graphical models remains challenging in high dimension due to the tremendous size of the model space. This article proposes a method to infer the marginal and…
Classical tests are available for the two-sample test of correspondence of distribution functions. From these, the Kolmogorov-Smirnov test provides also the graphical interpretation of the test results, in different forms. Here, we propose…
This paper proposes new tests of conditional independence of two random variables given a single-index involving an unknown finite-dimensional parameter. The tests employ Rosenblatt transforms and are shown to be distribution-free while…
The $X^2$ and $G^2$ tests are the most frequently applied tests for testing the independence of two categorical variables. However, no one, to the best of our knowledge has compared them, extensively, and ultimately answer the question of…
Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding…
Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the…
Temporal data are increasingly prevalent in modern data science. A fundamental question is whether two time series are related or not. Existing approaches often have limitations, such as relying on parametric assumptions, detecting only…
For testing two random vectors for independence, we consider testing whether the distance of one vector from a center point is independent from the distance of the other vector from a center point by a univariate test. In this paper we…
Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…