The excess-mass ellipsoid
The excess-mass ellipsoid is the ellipsoid that maximizes the difference between its probability content and a constant multiple of its volume, over all ellipsoids. When an empirical distribution determines the probability content, the sample excess-mass ellipsoid is a random set that can be used in contour estimation and tests for multimodality. Algorithms for computing the ellipsoid are provided, as well as comparative simulations. The asymptotic distribution of the parameters for the sample excess-mass ellipsoid are derived. It is found that a n1/3 normalization of the center of the ellipsoid and lengths of its axes converge in distribution to the maximizer of a Gaussian process with quadratic drift. The generalization of ellipsoids to convex sets is discussed.
Year of publication: |
1991
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Authors: | Nolan, D. |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 39.1991, 2, p. 348-371
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Publisher: |
Elsevier |
Keywords: | test for bimodality contour estimation minimum volume ellipsoid cube-root asymptotics empirical process Gaussian process quadratic drift nearest-neighbor distance rates of convergence |
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