Asymptotic theory for density ridges

DOI10.1214/15-AOS1329zbMath1327.62303arXiv1406.5663OpenAlexW3102707117MaRDI QIDQ888497

Yen-Chi Chen, Christopher R. Genovese, Larry Alan Wasserman

Publication date: 30 October 2015

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.5663

zbMATH Keywords

bootstrapridgeempirical processdensity estimationnonparametric statistics

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Nonparametric tolerance and confidence regions (62G15)

Related Items

Nonparametric modal regression, On nonparametric ridge estimation for multivariate long-memory processes, Theoretical analysis of nonparametric filament estimation, Solution manifold and its statistical applications, Classification methods for Hilbert data based on surrogate density, Posterior contraction and credible sets for filaments of regression functions, Asymptotic theory for density ridges, Bootstrapping max statistics in high dimensions: near-parametric rates under weak variance decay and application to functional and multinomial data, Empirical evolution equations, Statistical embedding: beyond principal components, Multiple penalized principal curves: analysis and computation, Beyond Gaussian approximation: bootstrap for maxima of sums of independent random vectors, Nonparametric inference via bootstrapping the debiased estimator, Toroidal PCA via density ridges, Unnamed Item, A comprehensive approach to mode clustering, Asymptotic confidence regions for density ridges, Generalized cluster trees and singular measures, Univariate log-concave density estimation with symmetry or modal constraints, Importance sampling and its optimality for stochastic simulation models, Normal-Bundle Bootstrap

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Theoretical analysis of nonparametric filament estimation
• Manifold estimation and singular deconvolution under Hausdorff loss
• Nonparametric ridge estimation
• Gaussian approximation of suprema of empirical processes
• Anti-concentration and honest, adaptive confidence bands
• Generalized density clustering
• Stability of persistence diagrams
• Asymptotic theory for density ridges
• On weak convergence and optimality of kernel density estimates of the mode
• Bootstrap methods: another look at the jackknife
• Properties of ridges and cores for two-dimensional images
• Ridges in image and data analysis
• On nonparametric estimation of density level sets
• Granulometric smoothing
• Curve reconstruction from noisy samples
• Bootstrapping the mode
• Rates of strong uniform consistency for multivariate kernel density estimators. (Vitesse de convergence uniforme presque sûre pour des estimateurs à noyaux de densités multivariées)
• Curve reconstruction from unorganized points
• Comparison and anti-concentration bounds for maxima of Gaussian random vectors
• The topography of multivariate normal mixtures
• Tokunaga and Horton self-similarity for level set trees of Markov chains
• Uniform in bandwidth consistency of kernel-type function estimators
• Local Likelihood Tracking of Fault Lines and Boundaries
• Properties of Minimizers of Average-Distance Problem via Discrete Approximation of Measures
• Statistical Analysis of Metric Graph Reconstruction
• The Structure and Stability of Persistence Modules
• Curvature Measures
• PLUG-IN ESTIMATION OF GENERAL LEVEL SETS
• The Geometry of Nonparametric Filament Estimation
• Proximity of persistence modules and their diagrams
• Metric graph reconstruction from noisy data
• Minimax Manifold Estimation
• Theory of Random Sets
• An empirical process approach to the uniform consistency of kernel-type function estimators
• New concentration inequalities in product spaces