Analytical and statistical properties of local depth functions motivated by clustering applications

DOI10.1214/23-EJS2110MaRDI QIDQ2689597

Claudio Agostinelli, Anand N. Vidyashankar, Alicia Nieto-Reyes, Giacomo Francisci

Publication date: 13 March 2023

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.11957

zbMATH Keywords

clusteringgradient systemmodesuniform central limit theoremHoeffding's decompositionlocal depthextreme localizationLyapunov's stability theoremsample local depth

Mathematics Subject Classification ID

Statistics (62-XX)

Uses Software

• KernSmooth

Cites Work

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• The central limit theorem for empirical processes on Vapnik- Červonenkis classes
• Local depth
• Limit theorems for \(U\)-processes
• On a notion of data depth based on random simplices
• A Bernstein-type inequality for \(U\)-statistics and \(U\)-processes
• A population background for nonparametric density-based clustering
• General notions of statistical depth function.
• Structural properties and convergence results for contours of sample statistical depth functions.
• Mixture model modal clustering
• Multiscale geometric feature extraction for high-dimensional and non-Euclidean data with applications
• Uniform in bandwidth consistency of kernel-type function estimators
• Consistent selection of the number of clusters via crossvalidation
• Lens data depth and median
• Mathematical Foundations of Infinite-Dimensional Statistical Models
• The estimation of the gradient of a density function, with applications in pattern recognition
• A Graph-Theoretic Approach to Nonparametric Cluster Analysis
• Model-Based Clustering, Discriminant Analysis, and Density Estimation
• β-Skeleton depth functions and medians
• Uniform Central Limit Theorems
• Comparison of Smoothing Parameterizations in Bivariate Kernel Density Estimation
• Persistence-Based Clustering in Riemannian Manifolds
• A Review on Modal Clustering

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