Smoothed log-concave maximum likelihood estimation with applications

Details Smoothed log-concave maximum likelihood estimation with applications Smoothed log-concave maximum likelihood estimation with applications

2011-02-06

arxiv.org/abs/1102.1191v3

Mathematics

Statistics Theory

30 pages, 5 figures

Scientific paper

We study the smoothed log-concave maximum likelihood estimator of a probability distribution on $\mathbb{R}^d$. This is a fully automatic nonparametric density estimator, obtained as a canonical smoothing of the log-concave maximum likelihood estimator. We demonstrate its attractive features both through an analysis of its theoretical properties and a simulation study. Moreover, we show how the estimator can be used as an intermediate stage of more involved procedures, such as constructing a classifier or estimating a functional of the density. Here again, the use of the estimator can be justified both on theoretical grounds and through its finite sample performance, and we illustrate its use in a breast cancer diagnosis (classification) problem.

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