Related papers: Dimension-agnostic inference using cross U-statist…
Inference in clustering is paramount to uncovering inherent group structure in data. Clustering methods which assess statistical significance have recently drawn attention owing to their importance for the identification of patterns in high…
For nonparametric inference about a function, multiscale testing procedures resolve the need for bandwidth selection and achieve asymptotically optimal detection performance against a broad range of alternatives. However, critical values…
An overwhelming majority of experiments in classical and quantum physics make a priori assumptions about the dimension of the system under consideration. However, would it be possible to assess the dimension of a completely unknown system…
We establish normal approximation in the Wasserstein metric for both non-degenerate and degenerate second-order U-statistics under cross-sectional dependence using Stein's method. For the non-degenerate case, our results extend recent…
The two-sample problem, which consists in testing whether independent samples on $\mathbb{R}^d$ are drawn from the same (unknown) distribution, finds applications in many areas. Its study in high-dimension is the subject of much attention,…
We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different mean vectors. A stochastic representation for the…
Traditional meta-analysis assumes that the effect sizes estimated in individual studies follow a Gaussian distribution. However, this distributional assumption is not always satisfied in practice, leading to potentially biased results. In…
The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…
This paper takes a different look on the problem of testing the mutual independence of the components of a high-dimensional vector. Instead of testing if all pairwise associations (e.g. all pairwise Kendall's $\tau$) between the components…
We propose a novel statistical method for testing the results of anomaly detection (AD) under domain adaptation (DA), which we call CAD-DA -- controllable AD under DA. The distinct advantage of the CAD-DA lies in its ability to control the…
Violation of the assumptions underlying classical (Gaussian) limit theory often yields unreliable statistical inference. This paper shows that the bootstrap can detect such violations by delivering simple and powerful diagnostic tests that…
Multivariate elliptically-contoured distributions are widely used for modeling correlated and non-Gaussian data. In this work, we study the kurtosis of the elliptical model, which is an important parameter in many statistical analysis.…
In this paper, we study a method to sample from a target distribution $\pi$ over $\mathbb{R}^d$ having a positive density with respect to the Lebesgue measure, known up to a normalisation factor. This method is based on the Euler…
Testing for change points in sequences of covariance matrices is an important and equally challenging problem in statistical methodology with applications in various fields. Motivated by the observation that even in cases where the ratio…
We derive exceedingly simple practical procedures revealing the quantum nature of states and measurements by the violation of classical upper bounds on the statistics of arbitrary measurements. Data analysis is minimum and definite…
Heisenberg's uncertainty principle is often cited as an example of a "purely quantum" relation with no analogue in the classical limit where $\hbar \to 0$. However, this formulation of the classical limit is problematic for many reasons,…
This paper develops a general framework for analyzing asymptotics of $V$-statistics. Previous literature on limiting distribution mainly focuses on the cases when $n \to \infty$ with fixed kernel size $k$. Under some regularity conditions,…
The consistency of doubly robust estimators relies on consistent estimation of at least one of two nuisance regression parameters. In moderate to large dimensions, the use of flexible data-adaptive regression estimators may aid in achieving…
It is well known that non-parametric methods suffer from the "curse of dimensionality". We propose here a new estimation method for a multivariate distribution, using sub-sampling and ranks, which seems not to suffer from this "curse". We…
To assess whether there is some signal in a big database, aggregate tests for the global null hypothesis of no effect are routinely applied in practice before more specialized analysis is carried out. Although a plethora of aggregate tests…