# Maximum likelihood estimation of a multidimensional log-concave density

@article{Cule2008MaximumLE, title={Maximum likelihood estimation of a multidimensional log-concave density}, author={Madeleine L. Cule and Richard J. Samworth and Michael I. Stewart}, journal={arXiv: Methodology}, year={2008} }

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…

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