Related papers: A consistent multivariate test of association base…
Shape constraints yield flexible middle grounds between fully nonparametric and fully parametric approaches to modeling distributions of data. The specific assumption of log-concavity is motivated by applications across economics, survival…
High-dimensional phenotypes hold promise for richer findings in association studies, but testing of several phenotype traits aggravates the grand challenge of association studies, that of multiple testing. Several methods have recently been…
We study a novel class of affine invariant and consistent tests for multivariate normality. The tests are based on a characterization of the standard $d$-variate normal distribution by means of the unique solution of an initial value…
The aim of this thesis is to find a solution to the non-parametric independence problem in separable metric spaces. Suppose we are given finite collection of samples from an i.i.d. sequence of paired random elements, where each marginal has…
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…
We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance--covariance matrices, and the other is on off-diagonal sub-matrices, which define the covariance…
The most popular ways to test for independence of two ordinal random variables are by means of Kendall's tau and Spearman's rho. However, such tests are not consistent, only having power for alternatives with ``monotonic'' association. In…
Many commonly used test statistics are based on a norm measuring the evidence against the null hypothesis. To understand how the choice of a norm affects power properties of tests in high dimensions, we study the consistency sets of…
Real-world data typically contain a large number of features that are often heterogeneous in nature, relevance, and also units of measure. When assessing the similarity between data points, one can build various distance measures using…
In this paper, we develop invariance-based procedures for testing and inference in high-dimensional regression models. These procedures, also known as randomization tests, provide several important advantages. First, for the global null…
Optimal transport and Wasserstein distances are flourishing in many scientific fields as a means for comparing and connecting random structures. Here we pioneer the use of an optimal transport distance between L\'{e}vy measures to solve a…
When applying multivariate extreme value statistics to analyze tail risk in compound events defined by a multivariate random vector, one often assumes that all dimensions share the same extreme value index. While such an assumption can be…
We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the…
We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete or mixture of those, with light tails or heavy…
We generalize the optimal coupling theorem to multiple random variables: Given a collection of random variables, it is possible to couple all of them so that any two differ with probability comparable to the total-variation distance between…
Distance covariance is a widely used statistical methodology for testing the dependency between two groups of variables. Despite the appealing properties of consistency and superior testing power, the testing results of distance covariance…
In this paper, we consider testing the martingale difference hypothesis for high-dimensional time series. Our test is built on the sum of squares of the element-wise max-norm of the proposed matrix-valued nonlinear dependence measure at…
The aim of this paper is to show a possibility to identify multivariate distribution by means of specially constructed one-dimensional random variable. We give some inequalities which may appear to helpful for a construction of multivariate…
Log-linear models are a family of probability distributions which capture relationships between variables. They have been proven useful in a wide variety of fields such as epidemiology, economics and sociology. The interest in using these…
This paper is concerned with all tests for continuous-variable entanglement that arise from linear combinations of second moments or variances of canonical coordinates, as they are commonly used in experiments to detect entanglement. All…