A note on estimation of the shape of density level sets of star-shaped distributions
| Autor: | Hidehiko Kamiya |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
021103 operations research Mathematical analysis Kernel density estimation 0211 other engineering and technologies Strong consistency Estimator Multivariate normal distribution 02 engineering and technology Star (graph theory) 01 natural sciences Ellipsoid Exponential function 010104 statistics & probability Hausdorff distance 0101 mathematics Mathematics |
| Zdroj: | Communications in Statistics - Theory and Methods. 48:3092-3104 |
| ISSN: | 1532-415X 0361-0926 |
| DOI: | 10.1080/03610926.2018.1473606 |
| Popis: | Elliptically contoured distributions generalize the multivariate normal distributions in such a way that the density generators need not be exponential. However, as the name suggests, elliptically contoured distributions remain to be restricted in that the proportional density level sets ought to be ellipsoids. In star-shaped distributions, this restriction is relaxed and the density level sets are allowed to be boundaries of arbitrary proportional star-shaped sets. In this note, we propose a non parametric estimator of the shape of density level sets of star-shaped distributions, and prove its strong consistency with respect to the Hausdorff distance. We illustrate our estimator with simulated and real data. |
| Databáze: | OpenAIRE |
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