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Density Estimation under Qualitative Assumptionsin Higher Dimensions

Polonik, Wolfgong

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Abstract

We study a method for estimating a density f in the d-dimensional Euclidean space under assumptions which are of qualitative nature. The resulting density estimator can be considered as a generalization of the Grenander estimator for monotone densities. The assumptions on f are given in terms of the density contour clusters. We assume that the density contourclusters lie in a given class of measurable subsets of the d-dimensionalEuclidean space. By choosing this class appropriately it is possible tomodel for example monotonicity, symmetry or multimodality. The mainmathematical tool for proving consistency and rates of convergence of thedensity estimator is empirical process theory.

Item Type: Working paper
Place of Publication: Heidelberg
Date Deposited: 20 Jun 2016 07:25
Date: 1995
Number of Pages: 33
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Schriftenreihe ID: Beiträge zur Statistik > Beiträge
Additional Information: auch erschienen in: Journal of Multivariate Analysis 55, No. 1 (1995), 61-81
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