GLOBAL RATES OF CONVERGENCE OF THE MLES OF LOG-CONCAVE AND s-CONCAVE DENSITIES

• 成果类型: Article
• 署名作者: Doss, Charles R.; Wellner, Jon A.
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; University of Washington; University of Washington Seattle
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1394
• 发表日期: 2016
• 页码: 954-981
• 关键词: maximum-likelihood-estimation; approximation; distributions; inequalities

摘要

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 < infinity 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.