Related papers: Test of Bivariate Independence Based on Angular Pr…
We examine the distributions of non-commutative polynomials of non-atomic, freely independent random variables. In particular, we obtain an analogue of the Strong Atiyah Conjecture for free groups thus proving that the measure of each atom…
We propose the Cyclic Permutation Test (CPT) to test general linear hypotheses for linear models. This test is non-randomized and valid in finite samples with exact Type I error $\alpha$ for an arbitrary fixed design matrix and arbitrary…
Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite set. In this article, we consider a probability distribution generated by an infinite system of…
In general, randomness tests included in a test suite are not independent of each other. This renders it difficult to fix a rational criterion through the whole test suite with an explicit significance level. In this paper, we focus on the…
Independence and Conditional Independence (CI) are two fundamental concepts in probability and statistics, which can be applied to solve many central problems of statistical inference. There are many existing independence and CI measures…
Conditional randomization tests (CRTs) assess whether a variable $x$ is predictive of another variable $y$, having observed covariates $z$. CRTs require fitting a large number of predictive models, which is often computationally…
The free convolution is the binary operation on the set of probability measures on the real line which allows to deduce, from the individual spectral distributions, the spectral distribution of a sum of independent unitarily invariant…
We study properties of two resampling scenarios: Conditional Randomisation and Conditional Permutation schemes, which are relevant for testing conditional independence of discrete random variables $X$ and $Y$ given a random variable $Z$.…
Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…
Joint probabilistic modeling is essential for forecasting irregular multivariate time series (IMTS) to accurately quantify uncertainty. Existing approaches often struggle to balance model expressivity with consistent marginalization,…
Testing the equality of two high-dimensional mean vectors is a fundamental problem in multivariate analysis. While the classical Hotelling's $T^2$ test is optimal in low-dimensional settings, it fails when the dimension $p$ is comparable to…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
We propose notions of calibration for probabilistic forecasts of general multivariate quantities. Probabilistic copula calibration is a natural analogue of probabilistic calibration in the univariate setting. It can be assessed empirically…
We consider a non-Hermitian random matrix $A$ whose distribution is invariant under the left and right actions of the unitary group. The so-called Single Ring Theorem, proved by Guionnet, Krishnapur and Zeitouni, states that the empirical…
We introduce nonparametric tests of independence for bivariate circular data based on trigonometric moments. Our contributions lie in (i) proposing nonparametric tests that are locally and asymptotically optimal against bivariate cosine von…
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…
Describing statistical dependencies is foundational to empirical scientific research. For uncovering intricate and possibly non-linear dependencies between a single target variable and several source variables within a system, a principled…
We introduce ART, a distribution-free and model-agnostic framework for changepoint detection that provides finite-sample guarantees. ART transforms independent observations into real-valued scores via a symmetric function, ensuring…
Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is…
A new test of independence between random elements is presented in this article. The test is based on a functional of the Cram\'{e}r-von Mises type, which is applied to a $U$-process that is defined from the recurrence rates. Theorems of…