GLOBAL RATES OF CONVERGENCE OF THE MLES OF LOG-CONCAVE AND s-CONCAVE DENSITIES.
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ABSTRACT:
SUBMITTER: Doss CR
PROVIDER: S-EPMC5619328 | biostudies-literature | 2016
REPOSITORIES: biostudies-literature
Publications
GLOBAL RATES OF CONVERGENCE OF THE MLES OF LOG-CONCAVE AND <i>s</i>-CONCAVE DENSITIES.
Doss Charles R CR Wellner Jon A JA
Annals of statistics 20160411 3
We establish global rates of convergence for the Maximum Likelihood Estimators (MLEs) of log-concave and <i>s</i>-concave densities on ℝ. The main finding is that the rate of convergence of the MLE in the Hellinger metric is no worse than <i>n</i><sup>-2/5</sup> when -1 < <i>s</i> < ∞ where <i>s</i> = 0 corresponds to the log-concave case. We also show that the MLE does not exist for the classes of <i>s</i>-concave densities with <i>s</i> < -1. ...[more]
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