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arXiv · 2310.13478

Statistical depth and support medians for fuzzy data

Luis González-De La Fuente·Alicia Nieto-Reyes·Pedro Terán
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Abstract

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 real line by the median, they provide a natural approach to defining median-like location estimators for more general types of data (in our case, fuzzy data). We analyze the relationships between depth-based medians, medians based on the support function, and some notions of a median for fuzzy data in the literature. We take advantage of specific depth functions for fuzzy data defined in our former papers: adaptations of Tukey depth, simplicial depth, $L^1$-depth and projection depth.

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Luis González-De La Fuente, Alicia Nieto-Reyes, Pedro Terán. 2023-10-20. Statistical depth and support medians for fuzzy data. https://arxiv.org/abs/2310.13478

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