摘要翻译：
研究了对数凹概率密度的非参数极大似然估计及其分布和危险函数。这些估计量的一些一般性质是由两个刻划导出的。证明了在一定的正则性假设下，密度和危险率估计量关于紧区间上确界范数的收敛速度至少为$(\log(n)/n)^{1/3}$和典型的$(\log(n)/n)^{2/5}$,而经验分布函数与估计分布函数之间的差值随速度$O_{mathrm{p}}(n^{-1/2}）而消失。
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英文标题：
《Maximum likelihood estimation of a log-concave density and its
  distribution function: Basic properties and uniform consistency》
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作者：
Lutz Duembgen, Kaspar Rufibach
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最新提交年份：
2009
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  We study nonparametric maximum likelihood estimation of a log-concave probability density and its distribution and hazard function. Some general properties of these estimators are derived from two characterizations. It is shown that the rate of convergence with respect to supremum norm on a compact interval for the density and hazard rate estimator is at least $(\log(n)/n)^{1/3}$ and typically $(\log(n)/n)^{2/5}$, whereas the difference between the empirical and estimated distribution function vanishes with rate $o_{\mathrm{p}}(n^{-1/2})$ under certain regularity assumptions.
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PDF链接：
https://arxiv.org/pdf/709.0334