Related papers: A Shift Test for Independence in Generic Time Seri…
Analyzing the covariance structure of data is a fundamental task of statistics. While this task is simple for low-dimensional observations, it becomes challenging for more intricate objects, such as multivariate functions. Here, the…
We propose a test of independence of two multivariate random vectors, given a sample from the underlying population. Our approach, which we call MINT, is based on the estimation of mutual information, whose decomposition into joint and…
Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is…
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…
This article deals with the problem of testing conditional independence between two random vectors ${\bf X}$ and ${\bf Y}$ given a confounding random vector ${\bf Z}$. Several authors have considered this problem for multivariate data.…
The McNemar test evaluates the hypothesis that two correlated proportion is common in $2 \times 2$ contingency tables with the same categories. This study discusses a test for symmetry in $2 \times 2$ contingency tables with nonignorable…
The aim of sequential change-point detection is to issue an alarm when it is thought that certain probabilistic properties of the monitored observations have changed. This work is concerned with nonparametric, closed-end testing procedures…
Testing for the presence of autocorrelation is a fundamental problem in time series analysis. Classical methods such as the Box-Pierce test rely on the assumption of stationarity, necessitating the removal of non-stationary components such…
It has been recently shown in Jaworski, P., Jelito, D. and Pitera, M. (2024), 'A note on the equivalence between the conditional uncorrelation and the independence of random variables', Electronic Journal of Statistics 18(1), that one can…
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.…
Binomial time series in which the logit of the probability of success is modelled as a linear function of observed regressors and a stationary latent Gaussian process are considered. Score tests are developed to first test for the existence…
Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We introduce non-parametric test statistics, which are rescaled general…
We investigate the large-sample behavior of change-point tests based on weighted two-sample U-statistics, in the case of short-range dependent data. Under some mild mixing conditions, we establish convergence of the test statistic to an…
Some problems of statistics can be reduced to extremal problems of minimizing functionals of smooth functions defined on the cube $[0,1]^m$, $m\geq 2$. In this paper, we study a class of extremal problems that is closely connected to the…
Given a random sample of size $n$ from a $p$ dimensional random vector, where both $n$ and $p$ are large, we are interested in testing whether the $p$ components of the random vector are mutually independent. This is the so-called complete…
Information theory provides ideas for conceptualising information and measuring relationships between objects. It has found wide application in the sciences, but economics and finance have made surprisingly little use of it. We show that…
This article proposes a new index for quantifying the degree of dependence between random vectors. The index takes values in [0,1] and equals zero if and only if the random vectors are sub-independent. Unlike mere uncorrelatedness,…
Conformal prediction offers a practical framework for distribution-free uncertainty quantification, providing finite-sample coverage guarantees under relatively mild assumptions on data exchangeability. However, these assumptions cease to…
In this paper, we study the independence of shifts defined on $\mathbb{N}^d$ ($\mathbb{N}^d$ shift) and trees (tree-shift). Firstly, for the completeness of the article, we provide a proof that an $\mathbb{N}^d$ shift has positive…
We show that approximations of strict order can calibrate the fine structure of genericity. Particularly, we find exponential behavior within the $\mathrm{NSOP}_{n}$ hierarchy from model theory. Let $0$-$\eth$-independence denote…