A plug-in approach to support estimation. (English) Zbl 0897.62034

Summary: We suggest a new approach, based on the use of density estimators, for the problem of estimating the (compact) support of a multivariate density. This subject, motivated in terms of pattern analysis by U. Grenander [Abstract inference. (1981; Zbl 0505.62069)] has interesting connections with detection and clustering.
A natural class of density-based estimators is defined. Universal consistency results and convergence rates are established for these estimators, with respect to the usual measure-based metric \(d_\mu\) between sets. Further convergence rates (with respect to both \(d_\mu\) and the Hausdorff metric \(d_H\)) are also obtained under some, fairly intuitive, shape restrictions.


62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference


Zbl 0505.62069
Full Text: DOI


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