论文标题
使用分散的Conway-Maxwell-Poisson内核一致的二阶离散内核平滑
Consistent second-order discrete kernel smoothing using dispersed Conway-Maxwell-Poisson kernels
论文作者
论文摘要
离散概率质量函数的直方图估计量通常表现出与观察到的计数范围内和外部内的零概率估计相关的不良属性。为了避免这种情况，我们根据最近开发的均值份量的Conway--Maxwell-Poisson分布制定了一种新型的二阶离散核更平滑，该分布既可以过度分散和下分散。引入了两种自动带宽选择方法，一种基于kullback-leibler Divergence的简单最小化，另一种基于基于计算更高的交叉验证标准的方法。两种方法均表现出出色的小样本和大样本性能。来自一系列目标分布的模拟数据集上的计算结果说明了所提出方法与现有平滑且不平滑的估计器相比的灵活性和准确性。该方法应用于earth中的体积计数的建模，以及Hura树上的害虫的发育天数。
The histogram estimator of a discrete probability mass function often exhibits undesirable properties related to zero probability estimation both within the observed range of counts and outside into the tails of the distribution. To circumvent this, we formulate a novel second-order discrete kernel smoother based on the recently developed mean-parametrized Conway--Maxwell--Poisson distribution which allows for both over- and under-dispersion. Two automated bandwidth selection approaches, one based on a simple minimization of the Kullback--Leibler divergence and another based on a more computationally demanding cross-validation criterion, are introduced. Both methods exhibit excellent small- and large-sample performance. Computational results on simulated datasets from a range of target distributions illustrate the flexibility and accuracy of the proposed method compared to existing smoothed and unsmoothed estimators. The method is applied to the modelling of somite counts in earthworms, and the number of development days of insect pests on the Hura tree.
