在载体边界附近密度递减的NPMLE的行为
The behavior of the NPMLE of a decreasing density near the boundaries of the support
摘要：
我们研究的非参数最大似然估计$\hat{f}_n$的支持的边界附近的密度下降$f$的$f$的行为。我们建立了$\hat{f}_n(n^{-α})$的极限分布，其中我们需要区分$0<α<1$的不同值。对于有限支承的上端点也得到了类似的结果。这产生了一致的估计值的$f$的支持的边界。这些估计的极限分布的建立和他们的性能进行了比较与惩罚极大似然估计。
英文摘要：
We investigate the behavior of the nonparametric maximum likelihood estimator $\hat{f}_n$ for a decreasing density $f$ near the boundaries of the support of $f$. We establish the limiting distribution of $\hat{f}_n(n^{-α})$, where we need to distinguish between different values of $0<α<1$. Similar results are obtained for the upper endpoint of the support, in the case it is finite. This yields consistent estimators for the values of $f$ at the boundaries of the support. The limit distribution of these estimators is established and their performance is compared with the penalized maximum likelihood estimator.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
