## 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.

### MSC:

 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference

Zbl 0505.62069
Full Text:

### References:

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