In this paper we consider the stacking of isotonic regression and the method of rearrangement with the empirical estimator to estimate a discrete distribution with an infinite support. The estimators are proved to be strongly consistent with $\sqrt{n}$-rate of convergence. We obtain the asymptotic distributions of the estimators and construct the asymptotically correct conservative global confidence bands. We show that stacked Grenander estimator outperforms the stacked rearrangement estimator. The new estimators behave well even for small sized data sets and provide a trade-off between goodness-of-fit and shape constraints.

翻译：在本文中,我们考虑的是异质回归的堆叠和与经验估计器重新排列的方法,以便用无限的支持来估计离散分布。 估计器被证明非常符合$\sqrt{n}$的趋同率。 我们获得了测量器的无症状分布, 并构建了无症状正确的保守全球信任带。 我们显示,堆叠的Grenander 估测器比堆叠的重新排列估测器更完美。 新的估测器表现良好, 甚至对于小尺寸的数据集来说也是如此, 并且提供了优美和形状限制之间的权衡。