Related papers: Kernel-based independence and mean independence te…
In nonparametric independence testing, we observe i.i.d.\ data $\{(X_i,Y_i)\}_{i=1}^n$, where $X \in \mathcal{X}, Y \in \mathcal{Y}$ lie in any general spaces, and we wish to test the null that $X$ is independent of $Y$. Modern test…
We propose novel kernel-based tests for assessing the equivalence between distributions. Traditional goodness-of-fit testing is inappropriate for concluding the absence of distributional differences, because failure to reject the null…
We discuss how MultiFIT, the Multiscale Fisher's Independence Test for Multivariate Dependence proposed by Gorsky and Ma (2022), compares to existing linear-time kernel tests based on the Hilbert-Schmidt independence criterion (HSIC). We…
The concept of independence plays a crucial role in probability theory and has been the subject of extensive research in recent years. Numerous approaches have been proposed to test for independence; however, most of them address the…
Kernel techniques are among the most popular and powerful approaches of data science. Among the key features that make kernels ubiquitous are (i) the number of domains they have been designed for, (ii) the Hilbert structure of the function…
Asymptotic properties of a dimension-robust dependence measure are investigated. It is related to those used in independence tests, but is derivable, thus suitable for independent component analysis. An adjustable kernel allows to…
Measuring and testing the dependency between multiple random functions is often an important task in functional data analysis. In the literature, a model-based method relies on a model which is subject to the risk of model misspecification,…
In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These…
This paper introduces a decision-theoretic framework for constructing and evaluating test statistics based on their relationship with ancillary statistics-quantities whose distributions remain fixed under the null and alternative…
We propose a new multivariate dependency measure. It is obtained by considering a Gaussian kernel based distance between the copula transform of the given d-dimensional distribution and the uniform copula and then appropriately normalizing…
Two-sample and independence tests with the kernel-based MMD and HSIC have shown remarkable results on i.i.d. data and stationary random processes. However, these statistics are not directly applicable to non-stationary random processes, a…
We propose to investigate test statistics for testing homogeneity in reproducing kernel Hilbert spaces. Asymptotic null distributions under null hypothesis are derived, and consistency against fixed and local alternatives is assessed.…
Motivated by applications in biological science, we propose a novel test to assess the conditional mean dependence of a response variable on a large number of covariates. Our procedure is built on the martingale difference divergence…
In this paper, we study distance covariance, Hilbert-Schmidt covariance (aka Hilbert-Schmidt independence criterion [Gretton et al. (2008)]) and related independence tests under the high dimensional scenario. We show that the sample…
We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with…
We study the problem of testing the null hypothesis that X and Y are conditionally independent given Z, where each of X, Y and Z may be functional random variables. This generalises testing the significance of X in a regression model of…
In this paper, we propose a test for the equality of multiple distributions based on kernel mean embeddings. Our framework provides a flexible way to handle multivariate or even high-dimensional data by virtue of kernel methods and allows…
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…
Considering a regression model, we address the question of testing the nullity of the regression function. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…