论文标题
估计二维完全积极分布的最佳速率
Optimal Rates for Estimation of Two-Dimensional Totally Positive Distributions
论文作者
论文摘要
我们研究了二维完全积极分布的最小值估计。这种分布与非常肯定依赖的随机变量对，并且经常出现在统计和概率中。特别是，对于$β$-Hölder光滑密度的分布，其中$β\ in（0，2）$，我们观察到多条件上更快的估计速率，何时施加了总阳性条件。此外，我们展示了快速算法来计算提出的估计器并通过模拟研究证实了估计的理论速率。
We study minimax estimation of two-dimensional totally positive distributions. Such distributions pertain to pairs of strongly positively dependent random variables and appear frequently in statistics and probability. In particular, for distributions with $β$-Hölder smooth densities where $β\in (0, 2)$, we observe polynomially faster minimax rates of estimation when, additionally, the total positivity condition is imposed. Moreover, we demonstrate fast algorithms to compute the proposed estimators and corroborate the theoretical rates of estimation by simulation studies.
