GLOBAL RATES OF CONVERGENCE OF THE MLES OF LOG-CONCAVE AND s-CONCAVE DENSITIES.
GLOBAL RATES OF CONVERGENCE OF THE MLES OF LOG-CONCAVE AND s-CONCAVE DENSITIES.
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DOI：
10.1214/15-aos1394
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发表时间：
2016
影响因子：
4.5
通讯作者：
Wellner JA
中科院分区：
文献类型：
--
作者：
Doss CR;Wellner JA
我们建立了对数凹和s凹密度的最大似然估计（MLE）的全局收敛速度。主要的发现是，当−1 < s < ∞时，极大似然估计在海林格度量下的收敛速度不差于n−2/5，其中s = 0对应于对数凹的情况。我们还证明了对于s < −1的s-凹密度类，极大似然估计不存在。
We establish global rates of convergence for the Maximum Likelihood Estimators (MLEs) of log-concave and s-concave densities on 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 < ∞ 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.