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arXiv · 1306.1438

Global Rates of Convergence of the MLEs of Log-concave and s-concave Densities

Charles R. Doss·Jon A. Wellner
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Abstract

We establish global rates of convergence for the Maximum Likelihood Estimators (MLEs) of log-concave and $s$-concave densities on $\mathbb{R}$. The main finding is that the rate of convergence of the MLE in the Hellinger metric is no worse than $n^{-2/5}$ when $-1 < s < \infty$ where $s=0$ corresponds to the log-concave case. We also show that the MLE does not exist for the classes of $s$-concave densities with $s < - 1$.

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Charles R. Doss, Jon A. Wellner. 2013-06-06. Global Rates of Convergence of the MLEs of Log-concave and s-concave Densities. https://arxiv.org/abs/1306.1438

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