Optimal level sets for bivariate density representation
type: Item
instance of: scholarly article
title: Optimal level sets for bivariate density representation
zbMATH Open document ID: 1325.62038
author: Philippe Vieu
author: Pedro Delicado
published in: Journal of Multivariate Analysis
publication date: 2015-09-10T00:00:00Z
full work available at URL: http://hdl.handle.net/2117/86017
review text: For the bivariate density representation, there are a lot of results on level set estimation when the levels are fixed. The choice of levels is an important practical question and its answer requires both the definition of an optimal level and the construction of the method for finding it. Two scenarios of this problem are considered. The first one corresponds to a situation in which one has just a single density function to be represented. At the same time, the need arises to develop a joint representation for a lot of densities, and this is the second scenario of the paper. When the number of bivariate density functions to be represented is large, and when each density is recorded at a different time, a convenient way to represent them is using an animated graph, in which each image corresponds to the graph of each bivariate density. In this case each density by a few density level sets can be represented. Two approaches for quantifying the quality of a level set are developed. The first one uses distances between level sets and the second one is based on distances between density functions. In the paper, the consistency for the estimated levels is provided, and wide Monte Carlo simulated experiments illustrating the feasibility of the proposed method are presented.
reviewed by: Vyacheslav A. Vasiliev
Mathematics Subject Classification ID: 62E17
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 68R10
Mathematics Subject Classification ID: 94C15
Mathematics Subject Classification ID: 05C80
Mathematics Subject Classification ID: 65C60
zbMATH DE Number: 6480454
zbMATH Keywords: bivariate probability densities
zbMATH Keywords: optimal level sets for densities
zbMATH Keywords: graphical representation of bivariate densities
zbMATH Keywords: consistency estimators of levels
zbMATH Keywords: optimal representation of densities by level sets
describes a project that uses: R
describes a project that uses: KernSmooth
describes a project that uses: pdfTeX
describes a project that uses: LBFGS-B
describes a project that uses: fda (R)
MaRDI profile type: Publication
OpenAlex ID: W2042206293
cites work: Q4281870
cites work: Total error in a plug-in estimator of level sets.
cites work: Convergence rates in nonparametric estimation of level sets
cites work: Q4293547
cites work: Q4153971
cites work: Q3187976
cites work: Modern multidimensional scaling. Theory and applications.
cites work: Q4365239
cites work: Generalized multidimensional scaling: A framework for isometry-invariant partial surface matching
cites work: A Limited Memory Algorithm for Bound Constrained Optimization
cites work: Kernel estimation of density level sets
cites work: Minimum distance density-based estimation
cites work: Q3567508
cites work: Dimensionality reduction when data are density functions
cites work: Q3336497
cites work: Q4828421
cites work: Visual Error Criteria for Qualitative Smoothing
cites work: Asymptotic normality of plug-in level set estimates
cites work: Q3966921
cites work: Measuring mass concentrations and estimating density contour clusters -- An excess mass approach
cites work: Functional data analysis.
cites work: Nonparametric estimation of level sets under minimal assumptions
cites work: Q4727203
cites work: Smoothing methods in statistics
cites work: On nonparametric estimation of density level sets
cites work: Q4865051
DOI: 10.1016/J.JMVA.2015.04.005
description: scientific article; zbMATH DE number 6480454