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Measuring Mass Concentration and Estimating DensityContour Clusters - an Excess Mass Approach

Polonik, Wolfgang

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Abstract

By using empirical process theory we study a method addressed totesting for multimodality and estimating density contour clusters in higherdimensions. The method is based on the so-called excess mass. Given aprobability measure F and a class of sets in the d-dimensional Euclidean space, the excess mass is defined as the maximal difference between theF-measure and l times the Lebesgue measure of sets in the given class. The excess mass can be estimated by replacing F by the empirical measure. Thecorreponding maximizing sets can be used for estimating density contourclusters. Comparing excess masses over different classes yields informationabout the modality of the underlying probability measure. This can be usedto construct tests for multimodality. The asymptotic behaviour of theconsidered estimators and test statistics is studied for different classesof sets, including the classes of balls, ellipsoids and convex sets.

Item Type: Working paper
Place of Publication: Heidelberg
Date Deposited: 20 Jun 2016 09:03
Date: 1995
Number of Pages: 34
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 310 General statistics
510 Mathematics
Uncontrolled Keywords: Excess mass; density contour cluster; multimodality; empirical process theory; support estimation; convex hull
Schriftenreihe ID: Beiträge zur Statistik > Beiträge
Additional Information: auch erschienen in: Annals of Statistics, 1995, Vol. 23, No. 3, 855-881
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