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math.ST2023
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…
math.ST2023
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…