2020/11/23 by Alejandro Cholaquidis, Cholaquidis, Alejandro, Ricardo Fraiman +3 · 1 citation
Mathematics · #Boundary (topology) #Cartography #Combinatorics #Computer science #Consistency (knowledge bases) #Discrete mathematics #Estimator #FOS: Mathematics #Fuzzy Systems and Optimization #Geography #Geometry #Hausdorff dimension #Hausdorff measure #Intersection (aeronautics) #Mathematical analysis #Mathematics #Measure (data warehouse) #Metric (unit) #Metric space #Physics #Point (geometry) #Population #Sample (material) #Space (punctuation) #Statistics #Statistics Theory (math.ST) #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.2011.11146
openalex publication_date 2020/11/23 · arxiv created 2021/03/28 · arxiv updated 2021/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The lens depth of a point has been recently extended to general metric spaces, which is not the case for most depths. It is defined as the probability of being included in the intersection of two random balls centred at two random points X and Y, with the same radius d(X, Y). We study the consistency in Hausdorff and measure distance, of the level sets of the empirical lens depth, based on an iid sample on a general metric space. We also prove that the boundary of the empirical level sets are consistent estimators of their population counterparts, and analyze two real-life examples