Spatial quantiles on the hypersphere Page 1 The Annals of Statistics 2023, Vol. 51, No. 5,
2221–2245 https://doi.org/10.1214/23-AOS2332 © Institute of Mathematical Statistics, 2023 …

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 …

The distribution function is essential in statistical inference and connected with samples to
form a directed closed loop by the correspondence theorem in measure theory and the …

Statistical depth functions are a standard tool in nonparametric statistics to extend order-
based univariate methods to the multivariate setting. Since there is no universally accepted …

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 …

The popularity of transformer-based text embeddings calls for better statistical tools for
measuring distributions of such embeddings. One such tool would be a method for ranking …

Enthusiasm for Machine Learning is spreading to nearly all fields such as transportation,
energy, medicine, banking or insurance as the ubiquity of sensors through IoT makes more …

Statistical depth, a useful tool to measure the center-outward rank of multivariate and
functional data, is still under-explored in temporal point processes. Recent studies on point …

Non-Euclidean data is currently prevalent in many fields, necessitating the development of
novel concepts such as distribution functions, quantiles, rankings, and signs for these data in …

Depth measures have gained popularity in the statistical literature for defining level sets in
complex data structures like multivariate data, functional data, and graphs. Despite their …