Statistical analysis of measures of non-convexity

Alejandro Cholaquidis ^[1] ; Ricardo Fraiman ^[1] ; Leonardo Moreno ^[1] ; Beatriz Pateiro-López ^[2]
1. [1] Universidad de la República
  
  Universidad de la República
  
  Uruguay
2. [2] Universidade de Santiago de Compostela
  
  Universidade de Santiago de Compostela
  
  Santiago de Compostela, España
Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 33, Nº. 1, 2024, págs. 180-203
Idioma: inglés
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Resumen
- 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 others are more of topological nature. We address the statistical analysis of some of these measures of non-convexity of a set S, by dealing with their estimation based on a sample of points in S. We introduce also a new measure of non-convexity. We discuss briefly about these different notions of non-convexity, prove consistency and find the asymptotic distribution for the proposed estimators. We also consider the practical implementation of these estimators and illustrate their applicability to a real data example.