Related papers: Nonparametric statistics on manifolds with applica…
Let M be an analytic manifold modelled on an ultrametric Banach space over a complete ultrametric field. Let f be an analytic diffeomorphism from M onto itself and p be a fixed point of f. We discuss invariant manifolds around p, like…
This article provides an exposition of recent methodologies for nonparametric analysis of digital observations on images and other non-Euclidean objects. Fr\'echet means of distributions on metric spaces, such as manifolds and stratified…
We review recent developments on the characterization of random landscapes in high-dimension. We focus in particular on the problem of characterizing the landscape topology and geometry, discussing techniques to count and classify its…
Our goal is to extend information geometry to situations where statistical modeling is not obvious. The setting is that of modeling experimental data. Quite often the data are not of a statistical nature. Sometimes also the model is not a…
So-called linear rank statistics provide a means for distribution-free (even in finite samples), yet highly flexible, two-sample testing in the setting of univariate random variables. Their flexibility derives from a choice of weights that…
This article describes recent applications of algebraic geometry to noncommutative algebra. These techniques have been particularly successful in describing graded algebras of small dimension.
Information geometry is a mathematical framework that elucidates the manifold structure of the probability distribution space (p-space), providing a systematic approach to transforming probability distributions (PDs). In this study, we…
We investigate the distributional extension of the $k$-plane transform in $\mathbb{R}^d$ and of related operators. We parameterize the $k$-plane domain as the Cartesian product of the Stiefel manifold of orthonormal $k$-frames in…
Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
This survey explores a range of classical findings and recent developments related to our understanding of astheno-K\"ahler manifolds. Furthermore, we provide various examples of astheno-K\"ahler manifolds and analyze the challenges…
We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed process is a nonparametric transformation of an underlying parametric diffusion (UPD). This modelling strategy yields a general class…
A spatial point pattern is called anisotropic if its spatial structure depends on direction. Several methods for anisotropy analysis have been introduced in the literature. In this paper, we give an overview of nonparametric methods for…
We introduce an innovative method for incremental nonparametric probabilistic inference in high-dimensional state spaces. Our approach leverages \slices from high-dimensional surfaces to efficiently approximate posterior distributions of…
One of the data structures generated by medical imaging technology is high resolution point clouds representing anatomical surfaces. Raw images are in the form of triangulated surfaces and the first step is to create a standardised…
We introduce and investigate in this paper a new convenient method of introduction of a norm in the multidimensional rearrangement probability invariant space.
In this article, it is described how to use statistical data analysis to obtain models directly from data. The focus is put on finding nonlinearities within a generalized additive model. These models are found by the means of backfitting…
In recent years, several quantizations of real manifolds have been studied, in particular from the point of view of Connes' noncommutative geometry. Less is known for complex noncommutative spaces. In this paper, we review some recent…
In this article, we establish the mathematical foundations for modeling the randomness of shapes and conducting statistical inference on shapes using the smooth Euler characteristic transform. Based on these foundations, we propose two…
In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of their order. Thus, an $n$-sample in a space $M$ can be…