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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…
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…
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…