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Maximum likelihood estimation of a multidimensional log-concave density

Abstract:

Let X_1, ..., X_n be independent and identically distributed random vectors with a log-concave (Lebesgue) density f. We first prove that, with probability one, there exists a unique maximum likelihood estimator of f. The use of this estimator is attractive because, unlike kernel density estimation, the method is fully automatic, with no smoothing parameters to choose. Although the existence proof is non-constructive, we are able to reformulate the issue of computation in terms of a non-differ...

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Publication status:
Published

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Institution:
University of Oxford
Department:
Oxford, MPLS, Statistics
Role:
Author
Publisher:
Blackwell Publishing Ltd
Journal:
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
Volume:
72
Issue:
5
Pages:
545-607
Publication date:
2008-04-24
DOI:
EISSN:
1467-9868
ISSN:
1369-7412
URN:
uuid:6c893860-98a2-4b10-ad5d-bd3cea3d4427
Source identifiers:
97818
Local pid:
pubs:97818
Language:
English
Keywords:

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