2021/07/29 by Gery Geenens, Geenens, Gery, Alicia Nieto-Reyes +3 · 2 citations
Engineering · Mathematics · #Advanced Statistical Methods and Models #Artificial intelligence #Computer science #Data mining #Dimension (graph theory) #Engineering #Epistemology #FOS: Computer and information sciences #Flexibility (engineering) #Function (biology) #Function space #Mathematics #Measure (data warehouse) #Methodology (stat.ME) #Metric (unit) #Metric space #Property (philosophy) #Pure mathematics #Ranking (information retrieval) #Space (punctuation) #Statistics #Theoretical computer science #stat.ME
paper · pdf · doi:10.48550/arxiv.2107.13779
published in arXiv (Cornell University) (Cornell University)
arxiv created 2021/07/29 · openalex publication_date 2021/07/29 · arxiv updated 2021/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion a ranking of observations which is absent in more than one dimension. Motivated by the rapid development of technology, in particular the advent of `Big Data', we extend here that concept to general metric spaces, propose a natural depth measure and explore its properties as a statistical depth function. Working in a general metric space allows the depth to be tailored to the data at hand and to the ultimate goal of the analysis, a very desirable property given the polymorphic nature of modern data sets. This flexibility is thoroughly illustrated by several real data analyses.