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Statistical analysis of measures of non-convexity

Author

Listed:
  • Alejandro Cholaquidis

    (Universidad de la República)

  • Ricardo Fraiman

    (Universidad de la República)

  • Leonardo Moreno

    (Universidad de la República)

  • Beatriz Pateiro-López

    (Universidade de Santiago de Compostela)

Abstract

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.

Suggested Citation

  • Alejandro Cholaquidis & Ricardo Fraiman & Leonardo Moreno & Beatriz Pateiro-López, 2024. "Statistical analysis of measures of non-convexity," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(1), pages 180-203, March.
    • Handle: RePEc:spr:testjl:v:33:y:2024:i:1:d:10.1007_s11749-023-00889-4
    DOI: 10.1007/s11749-023-00889-4
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