二维完全正分布估计的最优速率
Optimal Rates for Estimation of Two-Dimensional Totally Positive Distributions
摘要：
研究二维完全正分布的极小极大估计。这种分布属于强正相关的随机变量对，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$β\in (0, 2)$，我们观察到多项式更快的极小极大估计率时，另外，总的积极性条件。此外，我们展示了快速算法来计算所提出的估计和证实的理论估计率的模拟研究。
英文摘要：
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.
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