Related papers: Kernel-based Tests for Joint Independence
This paper investigates the problem of testing independence of two random vectors of general dimensions. For this, we give for the first time a distribution-free consistent test. Our approach combines distance covariance with the…
We prove that kernel covariance embeddings lead to information-theoretically perfect separation of distinct continuous probability distributions. In statistical terms, we establish that testing for the \emph{equality} of two non-atomic…
We consider the problem of designing experiments to detect the presence of a specified heteroscedastity in a non-linear Gaussian regression model. In this framework, we focus on the ${\rm D}_s$- and KL-criteria and study their relationship…
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…
Recent years have witnessed growing concerns about the privacy of sensitive data. In response to these concerns, differential privacy has emerged as a rigorous framework for privacy protection, gaining widespread recognition in both…
Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare…
We introduce the Kernel Calibration Conditional Stein Discrepancy test (KCCSD test), a non-parametric, kernel-based test for assessing the calibration of probabilistic models with well-defined scores. In contrast to previous methods, our…
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…
There exist a number of tests for assessing the nonparametric heteroscedastic location-scale assumption. Here we consider a goodness-of-fit test for the more general hypothesis of the validity of this model under a parametric functional…
Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles,…
Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives…
We propose a kernel-based partial permutation test for checking the equality of functional relationship between response and covariates among different groups. The main idea, which is intuitive and easy to implement, is to keep the…
Conditional local independence is an asymmetric independence relation among continuous time stochastic processes. It describes whether the evolution of one process is directly influenced by another process given the histories of additional…
Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…
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…
In this paper the nonparametric quantile regression model is considered in a location-scale context. The asymptotic properties of the empirical independence process based on covariates and estimated residuals are investigated. In particular…
We propose a simple and intuitive test for arguably the most prevailing hypothesis in statistics that data are independent and identically distributed (IID), based on a newly introduced off-diagonal sequential U-process. This IID test is…
Penalized empirical risk minimization with a surrogate loss function is often used to learn a high-dimensional linear decision rule in classification problems. Although much of the literature focus on the generalization error, there is a…
We introduce kernel nonparametric tests for Lancaster three-variable interaction and for total independence, using embeddings of signed measures into a reproducing kernel Hilbert space. The resulting test statistics are straightforward to…
Considering two independent Poisson processes, we address the question of testing equality of their respective intensities. We first propose single tests whose test statistics are U-statistics based on general kernel functions. The…