24 citations · 34 across the 29 of their papers we have counts for
31 papers · 1 filter
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…
A bootstrap approach for testing invariance under parameterized group actions: orthogonal reflections and axial symmetry
Alejandro Cholaquidis, Juan Cuesta-Albertos, Ricardo Fraiman +1
Testing whether a multivariate distribution is invariant under an orthogonal transformation is a classical problem when the transformation is fixed in advance. We address a harder…
Estimating axial symmetry using random projections
Alejandro Cholaquidis, Ricardo Fraiman, Manuel Hernández-Banadik +1
We study the directions of axial symmetry of multivariate distributions and relate the measure or cardinality of this set to spherical symmetry. Under Carleman's condition, two ind…
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…
On consistent estimation of dimension values
Alejandro Cholaquidis, Antonio Cuevas, Beatriz Pateiro-López
The problem of estimating, from a random sample of points, the dimension of a compact subset of the Euclidean space is considered. The emphasis is put on consistency results in…
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…
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…
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…
Home range estimation under a restricted sampling scheme
Alejandro Cholaquidis, Ricardo Fraiman, Manuel Hernandez-Banadik
The analysis of animal movement has gained attention recently. New continuous-time models and statistical methods have been developed to estimate some sets related to their movemen…
On a general definition of the functional linear model
José R. Berrendero, Alejandro Cholaquidis, Antonio Cuevas
A general formulation of the linear model with functional (random) explanatory variable , and scalar response Y is proposed. It includes the standard functional…
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…
Estimation of surface area
Catherine Aaron, Alejandro Cholaquidis, Ricardo Fraiman
We study the problem of estimating the surface area of the boundary of a sufficiently smooth set when the available information is only a finite…
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…
A combined strategy for multivariate density estimation
Alejandro Cholaquidis, Ricardo Fraiman, Badih Ghattas +1
Non-linear aggregation strategies have recently been proposed in response to the problem of how to combine, in a non-linear way, estimators of the regression function (see for inst…
Set Estimation Under Biconvexity Restrictions
Alejandro Cholaquidis, Antonio Cuevas
A set in the Euclidean plane is said to be biconvex if, for some angle , all its sections along straight lines with inclination angles and are convex sets…
Robust Fusion Methods for Structured Big Data
Catherine Aaron, Alejandro Cholaquidis, Ricardo Fraiman +1
We address one of the important problems in Big Data, namely how to combine estimators from different subsamples by robust fusion procedures, when we are unable to deal with the wh…
Semi-supervised learning
Alejandro Cholaquidis, Ricardo Fraiman, Mariela Sued
Semi-supervised learning deals with the problem of how, if possible, to take advantage of a huge amount of not classified data, to perform classification, in situations when, typic…
Robust Fusion Methods for Big Data
Catherine Aaron, Alejandro Cholaquidis, Ricardo Fraiman +1
We address one of the important problems in Big Data, namely how to combine estimators from different subsamples by robust fusion procedures, when we are unable to deal with the wh…
Detection of low dimensionality and data denoising via set estimation techniques
Catherine Aaron, Alejandro Cholaquidis, Antonio Cuevas
This work is closely related to the theories of set estimation and manifold estimation. Our object of interest is a, possibly lower-dimensional, compact set $S \subset {\mathbb R}^…
Level sets and drift estimation for reflected Brownian motion with drift
Alejandro Cholaquidis, Ricardo Fraiman, Ernesto Mordecki +1
We consider the estimation of the drift and the level sets of the stationary distri- bution of a Brownian motion with drift, reflected in the boundary of a compact set $S\subset R^…
On boundary detection
Catherine Aaron, Alejandro Cholaquidis
Given a sample of a random variable supported by a smooth compact manifold , we propose a test to decide whether the boundary of is empty or not with no…