Zobrazeno 1 - 10
of 175
pro vyhledávání: '"Moreno, Leonardo A."'
We show how a Cram\'er-Wold theorem for a family of multivariate probability distributions can be used to generate a similar theorem for mixtures (convex combinations) of distributions drawn from the same family. Using this abstract result, we establ
Externí odkaz:
http://arxiv.org/abs/2410.22038
A new, very general, robust procedure for combining estimators in metric spaces is introduced GROS. The method is reminiscent of the well-known median of means, as described in \cite{devroye2016sub}. Initially, the sample is divided into $K$ groups.
Externí odkaz:
http://arxiv.org/abs/2402.15442
Statistical learning methods are widely utilized in tackling complex problems due to their flexibility, good predictive performance and its ability to capture complex relationships among variables. Additionally, recently developed automatic workflows
Externí odkaz:
http://arxiv.org/abs/2311.06681
Regression on manifolds, and, more broadly, statistics on manifolds, has garnered significant importance in recent years due to the vast number of applications for this type of data. Circular data is a classic example, but so is data in the space of
Externí odkaz:
http://arxiv.org/abs/2310.08209
The volume function V(t) of a compact set S\in R^d is just the Lebesgue measure of the set of points within a distance to S not larger than t. According to some classical results in geometric measure theory, the volume function turns out to be a poly
Externí odkaz:
http://arxiv.org/abs/2307.00373
Several measures of non-convexity (departures from convexity) have been introduced in the literature, both for sets and functions. Some of them are of geometric nature, while others are more of topological nature. We address the statistical analysis
Externí odkaz:
http://arxiv.org/abs/2211.11476
According to a well-known theorem of Cram\'er and Wold, if $P$ and $Q$ are two Borel probability measures on $\mathbb{R}^d$ whose projections $P_L,Q_L$ onto each line $L$ in $\mathbb{R}^d$ satisfy $P_L=Q_L$, then $P=Q$. Our main result is that, if $P
Externí odkaz:
http://arxiv.org/abs/2206.13612
Using some extensions of a theorem of Heppes on finitely supported discrete probability measures, we address the problems of classification and testing based on projections. In particular, when the support of the distributions is known in advance (as
Externí odkaz:
http://arxiv.org/abs/2201.07628
The reach of a set $M \subset \mathbb R^d$, also known as condition number when $M$ is a manifold, was introduced by Federer in 1959. The reach is a central concept in geometric measure theory, set estimation, manifold learning, among others areas. W
Externí odkaz:
http://arxiv.org/abs/2110.12208
We address the problem of testing for the invariance of a probability measure under the action of a group of linear transformations. We propose a procedure based on consideration of one-dimensional projections, justified using a variant of the Cram\'
Externí odkaz:
http://arxiv.org/abs/2109.01041