Classical multivariate statistics measures the outlyingness of a point by its Mahalanobis
distance from the mean, which is based on the mean and the covariance matrix of the data …

The concept of depth has proved very important for multivariate and functional data analysis,
as it essentially acts as a surrogate for the notion of ranking of observations which is absent …

We propose a novel measure of statistical depth, the metric spatial depth, for data residing in
an arbitrary metric space. The measure assigns high (low) values for points located near (far …

A new method for embedding metric space or kernel data, called robust kernel point
projection (RKPP), is presented. It is based on a robust generalization of multidimensional …

The lens depth of a point has been recently extended to general metric spaces, which is not
the case for most depths. It is defined as the probability of being included in the intersection …

In high-dimensional statistics, the manifold hypothesis presumes that the data lie near low-
dimensional structures, called manifolds. This assumption helps explain why machine …

The Supplement contains proofs and auxiliary results, additional simulations for the two-
sample test, additional simulations for distance profiles and transport ranks for multimodal …

The Oja depth (simplicial volume depth) is one of the classical statistical techniques for
measuring the central tendency of data in multivariate space. Despite the widespread …

Object data analysis is concerned with statistical methodology for datasets whose elements
reside in an arbitrary, unspecified metric space. In this work we propose the object shape, a …

We measure the Out-of-domain uncertainty in the prediction of Neural Networks using a
statistical notion called``Lens Depth''(LD) combined with Fermat Distance, which is able to …