3 papers
math.ST2024
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…
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…
math.ST2011
On statistical properties of sets fulfilling rolling-type conditions
Antonio Cuevas, Ricardo Fraiman, Beatriz Pateiro-López
Motivated by set estimation problems, we consider three closely related shape conditions for compact sets: positive reach, r-convexity and rolling condition. First, the relations b…