Bivariate density estimation using BV regularisation

The problem of bivariate density estimation is studied with the aim of finding the density function with the smallest number of local extreme values which is adequate with the given data. Adequacy is defined via Kuiper metrics. The concept of the taut-string algorithm which provides adequate approxi...

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Bibliographic Details
Published in:Computational statistics & data analysis Vol. 51; no. 12; pp. 5622 - 5634
Main Authors: Obereder, Andreas, Scherzer, Otmar, Kovac, Arne
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 15.08.2007
Elsevier Science
Elsevier
Series:Computational Statistics & Data Analysis
Subjects:
Density estimation
Exact sciences and technology
General topics
Mathematics
Modality
Multivariate analysis
Nonparametric inference
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Probability and statistics
Regularisation
Sciences and techniques of general use
Statistics
Regularisation
Density estimation
Modality
Data analysis
Triangulation
Approximation
Filtering
Statistical computation
Extreme value
Two-dimensional calculations
Density function
Approximation algorithm
ISSN:0167-9473, 1872-7352
Online Access:Get full text
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Summary:The problem of bivariate density estimation is studied with the aim of finding the density function with the smallest number of local extreme values which is adequate with the given data. Adequacy is defined via Kuiper metrics. The concept of the taut-string algorithm which provides adequate approximations with a small number of local extrema is generalised for analysing two- and higher dimensional data, using Delaunay triangulation and diffusion filtering. Results are based on equivalence relations in one dimension between the taut-string algorithm and the method of solving the discrete total variation flow equation. The generalisation and some modifications are developed and the performance for density estimation is shown.
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2007.04.019