Related papers: A test for dependence between two point processes …
Real-life data are often non-IID due to complex distributions and interactions, and the sensitivity to the distribution of samples can differ among learning models. Accordingly, a key question for any supervised or unsupervised model is…
The method of maximum entropy is quite a powerful tool to solve the generalized moment problem, which consists of determining the probability density of a random variable X from the knowledge of the expected values of a few functions of the…
Linear mixed-effects models are widely used in analyzing repeated measures data, including clustered and longitudinal data, where inferences of both fixed effects and variance components are of importance. Unlike the fixed effect inference…
Conditional Mutual Information (CMI) is a measure of conditional dependence between random variables X and Y, given another random variable Z. It can be used to quantify conditional dependence among variables in many data-driven inference…
This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The…
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…
The issue of variance components testing arises naturally when building mixed-effects models, to decide which effects should be modeled as fixed or random. While tests for fixed effects are available in R for models fitted with lme4, tools…
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…
The test of independence is a crucial component of modern data analysis. However, traditional methods often struggle with the complex dependency structures found in high-dimensional data. To overcome this challenge, we introduce a novel…
A framework for quantifying dependence between random vectors is introduced. With the notion of a collapsing function, random vectors are summarized by single random variables, called collapsed random variables in the framework. Using this…
Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation,…
Mutual information (MI) is a useful information-theoretic measure to quantify the statistical dependence between two random variables: $X$ and $Y$. Often, we are interested in understanding how the dependence between $X$ and $Y$ in one set…
Independence testing is a fundamental problem in statistical inference: given samples from a joint distribution $p$ over multiple random variables, the goal is to determine whether $p$ is a product distribution or is $\epsilon$-far from all…
The aim of this paper is to propose a methodology for testing general hypothesis in a Markovian setting with random sampling. A discrete Markov chain X is observed at random time intervals $\tau$ k, assumed to be iid with unknown…
Procedures in assessing the impact of serial dependency on performance analysis are usually built on parametrically specified models. In this paper, we propose a robust, nonparametric approach to carry out this assessment, by computing the…
In environmental sciences, it is often of interest to assess whether the dependence between extreme measurements has changed during the observation period. The aim of this work is to propose a statistical test that is particularly sensitive…
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 develop a new statistical procedure to test whether the dependence structure is identical between two groups. Rather than relying on a single index such as Pearson's correlation coefficient or Kendall's Tau, we consider the entire…
In this paper, the maximal nonlinear conditional correlation of two random vectors $X$ and $Y$ given another random vector $Z$, denoted by $\rho_1(X,Y|Z)$, is defined as a measure of conditional association, which satisfies certain…
Statistical distances quantifies the difference between two statistical constructs. In this article, we describe reference values for a distance between samples derived from the Kolmogorov-Smirnov statistic $D_{F,F'}$. Each measure of the…