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Based on two independent samples X_1,...,X_m and X_{m+1},...,X_n drawn from multivariate distributions with unknown Lebesgue densities p and q respectively, we propose an exact multiple test in order to identify simultaneously regions of…

Nonparametric tests for equality of multivariate distributions are frequently desired in research. It is commonly required that test-procedures based on relatively small samples of vectors accurately control the corresponding Type I Error…

Two-sample tests for multivariate data and non-Euclidean data are widely used in many fields. Parametric tests are mostly restrained to certain types of data that meets the assumptions of the parametric models. In this paper, we study a…

Repeated observations have become increasingly common in biomedical research and longitudinal studies. For instance, wearable sensor devices are deployed to continuously track physiological and biological signals from each individual over…

We consider the problem of two-sample testing in a semi-supervised setting with abundant unlabeled covariate data. Standard two-sample tests neglect covariate information, which has the potential to significantly boost performance. However,…

The bottom-up saliency, an early stage of humans' visual attention, can be considered as a binary classification problem between centre and surround classes. Discriminant power of features for the classification is measured as mutual…

A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density…

We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to…

In high dimensions, the classical Hotelling's $T^2$ test tends to have low power or becomes undefined due to singularity of the sample covariance matrix. In this paper, this problem is overcome by projecting the data matrix onto lower…

We propose exploiting symmetries (exact or approximate) of the Standard Model (SM) to search for physics Beyond the Standard Model (BSM) using the data-directed paradigm (DDP). Symmetries are very powerful because they provide two samples…

Non-probability samples become increasingly popular in survey statistics but may suffer from selection biases that limit the generalizability of results to the target population. We consider integrating a non-probability sample with a…

Data depths are score functions that quantify in an unsupervised fashion how central is a point inside a distribution, with numerous applications such as anomaly detection, multivariate or functional data analysis, arising across various…

The concept of median/consensus has been widely investigated in order to provide a statistical summary of ranking data, i.e. realizations of a random permutation $\Sigma$ of a finite set, $\{1,\; \ldots,\; n\}$ with $n\geq 1$ say. As it…

Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the…

The energy test is a powerful binning-free, multi-dimensional and distribution-free tool that can be applied to compare a measurement to a given prediction (goodness-of-fit) or to check whether two data samples originate from the same…

We propose a general approach to construct weighted likelihood estimating equations with the aim of obtain robust estimates. The weight, attached to each score contribution, is evaluated by comparing the statistical data depth at the model…

Large-scale, big-variant, high-quality data are crucial for developing robust and successful deep-learning models for medical applications since they potentially enable better generalization performance and avoid overfitting. However, the…

A two-sample hypothesis test is a statistical procedure used to determine whether the distributions generating two samples are identical. We consider the two-sample testing problem in a new scenario where the sample measurements (or sample…

Mediation analyses are a statistical tool for testing the hypothesis about how the relationship between two variables may be direct or indirect via a third variable. Assessing statistical significance has been an area of active research;…

For the task of relevance analysis, the conventional Tukey's test may be applied to the set of all pairwise comparisons. However, there were few studies that discuss both nonparametric k-sample comparisons and relevance analysis in high…