1 citations · 1 across the 16 of their papers we have counts for
19 papers
Conformal Robust Set Estimation
Alejandro Cholaquidis, Emilien Joly, Leonardo Moreno
We introduce a robust conformal prediction method based on the half-mass radius $\dP(x):=\inf\{r>0:P(B(x,r))>1/2\}$. Its empirical version is exactly the distance from a point to i…
Depth based trimmed means
Alejandro Cholaquidis, Ricardo Fraiman, Leonardo Moreno +1
Robust estimation of location is a fundamental problem in statistics, particularly in scenarios where data contamination by outliers or model misspecification is a concern. In univ…
Two statistical problems for multivariate mixture distributions
Ricardo Fraiman, Leonardo Moreno, Thomas Ransford
We address two important statistical problems: that of estimating mixtures of multivariate normal distributions and mixtures of -distributions based on univariate projections, a…
A Cramér-Wold theorem for mixtures
Ricardo Fraiman, Leonardo Moreno, Thomas Ransford
We show how a Cramér-Wold theorem for a family of multivariate probability distributions can be used to generate a similar theorem for mixtures (convex combinations) of distributio…
GROS: A General Robust Aggregation Strategy
Alejandro Cholaquidis, Emilien Joly, Leonardo Moreno
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 \ci…
Conformal inference for regression on Riemannian Manifolds
Alejandro Cholaquidis, Fabrice Gamboa, Leonardo Moreno
Regression on manifolds, and, more broadly, statistics on manifolds, has garnered significant importance in recent years due to the vast number of applications for non Euclidean da…
On the notion of polynomial reach: a statistical application
Alejandro Cholaquidis, Antonio Cuevas, Leonardo Moreno
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 i…
On standardness and the non-estimability of certain functionals of a set
Alejandro Cholaquidis, Leonardo Moreno, Beatriz Pateiro-López
Standardness is a popular assumption in the literature on set estimation. It also appears in statistical approaches to topological data analysis, where it is common to assume that…
Statistical analysis of measures of non-convexity
Alejandro Cholaquidis, Ricardo Fraiman, Leonardo Moreno +1
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 other…
A Cramér-Wold theorem for elliptical distributions
Ricardo Fraiman, Leonardo Moreno, Thomas Ransford
According to a well-known theorem of Cramér and Wold, if and are two Borel probability measures on whose projections onto each line in $\mathbb…
Universally consistent estimation of the reach
Alejandro Cholaquidis, Ricardo Fraiman, Leonardo Moreno
The reach of a set , also known as condition number when is a manifold, was introduced by Federer in 1959. The reach is a central concept in geometric me…
Application of the Cramér-Wold theorem to testing for invariance under group actions
Ricardo Fraiman, Leonardo Moreno, Thomas Ransford
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 o…
Weighted lens depth: Some applications to supervised classification
Alejandro Cholaquidis, Ricardo Fraiman, Fabrice Gamboa +1
Starting with Tukey's pioneering work in the 1970's, the notion of depth in statistics has been widely extended especially in the last decade. These extensions include high dimensi…
Level sets of depth measures in abstract spaces
Alejandro Cholaquidis, Ricardo Fraiman, Leonardo Moreno
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 inte…
Level set and density estimation on manifolds
Alejandro Cholaquidis, Ricardo Fraiman, Leonardo Moreno
We tackle the problem of the estimation of the level sets L_f(λ) of the density f of a random vector X supported on a smooth manifold M\subsetR^d , from an iid sample of X. To do t…
Sensitivity analysis in general metric spaces
Fabrice Gamboa, Thierry Klein, Agnès Lagnoux +1
In this paper, we introduce new indices adapted to outputs valued in general metric spaces. This new class of indices encompasses the classical ones; in particular, the so-called S…
Sensitivity indices for output on a Riemannian manifold
R. Fraiman, F. Gamboa, L. Moreno
In the context of computer code experiments, sensitivity analysis of a complicated input-output system is often performed by ranking the so-called Sobol indices. One reason of the…
Connecting pairwise spheres by depth: DCOPS
Ricardo Fraiman, Fabrice Gamboa, Leonardo Moreno
We extend the classical notion of the spherical depth in \mathbb{R}^k, to the important setup of data on a Riemannian manifold. We show that this notion of depth satisfies a set of…
On the classification problem for Poisson Point Processes
Alejandro Cholaquidis, Liliana Forzani, Pamela Llop +1
We study the binary classification problem for Poisson point processes, which are allowed to take values in a general metric space. The problem is tackled in two different ways: es…