5 papers
On the continuity of the Tukey depth function for fuzzy data
Luis González-De La Fuente, Alicia Nieto-Reyes, Pedro Terán
The practical use of statistical depth for fuzzy data requires regularity, inferential stability, and computational feasibility. This paper studies these aspects for the first time…
Projection depth and -type depths for fuzzy random variables
Luis González-De La Fuente, Alicia Nieto-Reyes, Pedro Terán
Statistical depth functions are a standard tool in nonparametric statistics to extend order-based univariate methods to the multivariate setting. Since there is no universally acce…
Statistical depth and support medians for fuzzy data
Luis González-De La Fuente, Alicia Nieto-Reyes, Pedro Terán
Statistical depth functions order the elements of a space with respect to their centrality in a probability distribution or dataset. Since many depth functions are maximized in the…
Simplicial depths for fuzzy random variables
Luis González-De La Fuente, Alicia Nieto-Reyes, Pedro Terán
The recently defined concept of a statistical depth function for fuzzy sets provides a theoretical framework for ordering fuzzy sets with respect to the distribution of a fuzzy ran…
Properties of statistical depth with respect to compact convex random sets. The Tukey depth
Luis González-De La Fuente, Alicia Nieto-Reyes, Pedro Terán
We study a statistical data depth with respect to compact convex random sets which is consistent with the multivariate Tukey depth and the Tukey depth for fuzzy sets. In doing so,…