Asymptotic normality of plug-in level set estimates

Abstract

We establish the asymptotic normality of the $G$-measure of the symmetric difference between the level set and a plug-in-type estimator of it formed by replacing the density in the definition of the level set by a kernel density estimator. Our proof will highlight the efficacy of Poissonization methods in the treatment of large sample theory problems of this kind.

Published in at http://dx.doi.org/10.1214/08-AAP569 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (5)

• Uniform in bandwidth consistency of kernel-type function estimators
• Optimal rates for plug-in estimators of density level sets
• Asymptotic normality of plug-in level set estimates
• Bandwidth choice for nonparametric classification
• The Hough transform estimator

Cited by in corpus (22)

• Asymptotic normality of plug-in level set estimates
• A Population Background for Nonparametric Density-Based Clustering
• Asymptotics and optimal bandwidth selection for highest density region estimation
• Testing Functional Inequalities
• Clusters and water flows: a novel approach to modal clustering through Morse theory
• Level sets estimation and Vorob'ev expectation of random compact sets
• Generalized Laplace Inference in Multiple Change-Points Models
• Optimal Ridge Detection using Coverage Risk
• Measuring Human Activity Spaces from GPS Data with Density Ranking and Summary Curves
• Generalized Cluster Trees and Singular Measures
• Change point analysis in non-stationary processes - a mass excess approach
• Asymptotics of Lower Dimensional Zero-Density Regions
• On efficient estimators of the proportion of true null hypotheses in a multiple testing setup
• Skeleton Clustering: Dimension-Free Density-based Clustering
• Asymptotics and Optimal Bandwidth for Nonparametric Estimation of Density Level Sets
• Minimax Hausdorff estimation of density level sets
• Level set estimation from projection measurements: Performance guarantees and fast computation
• Nonparametric Estimation of Surface Integrals on Level Sets
• Posterior Contraction and Credible Sets for Filaments of Regression Functions
• An Asymptotic Equivalence between the Mean-Shift Algorithm and the Cluster Tree
• A comparative simulation study of data-driven methods for estimating density level sets
• Nonparametric Confidence Regions for Level Sets: Statistical Properties and Geometry