论文标题
GRENANDER - 石估计器：在一般定向的无环图上对离散分布的约束估计堆叠的估计
Grenander--Stone estimator: stacked constrained estimation of a discrete distribution over a general directed acyclic graph
论文作者
论文摘要
在本文中，我们将等渗回归与Stone的基于交叉验证的方法相结合，以估算具有一般可计数支持的分布，并在其上定义了部分订单关系。我们证明，对于任何潜在的分布，得出其收敛速率，估计器与一维支持率非常一致，我们获得了元帅类型的不平等，以实现估计器的累积分布函数。此外，我们为估计器构建了渐近正确的保守全球置信频带。结果表明，首先，对于小型数据集，估算器的表现也不错，其次，在非异构基础分布的情况下，估算值优于表现，而当真实分布是等渗的情况下，它的性能几乎与Grenander估计器一样好。因此，新的估计器在概率预测的拟合优点，单调性和质量之间提供了权衡。我们将估计量应用于巴西内脏利什曼病的发达时间数据，从2007年$ $ $ $ 2014 $。
In this paper we integrate isotonic regression with Stone's cross-validation-based method to estimate a distribution with a general countable support with a partial order relation defined on it. We prove that the estimator is strongly consistent for any underlying distribution, derive its rate of convergence, and in the case of one-dimensional support we obtain Marshal-type inequality for cumulative distribution function of the estimator. Also, we construct the asymptotically correct conservative global confidence band for the estimator. It is shown that, first, the estimator performs good even for small sized data sets, second, the estimator outperforms in the case of non-isotonic underlying distribution, and, third, it performs almost as good as Grenander estimator when the true distribution is isotonic. Therefore, the new estimator provides a trade-off between goodness-of-fit, monotonicity and quality of probabilistic forecast. We apply the estimator to the time-to-onset data of visceral leishmaniasis in Brazil collected from $2007$ to $2014$.
