论文标题
部分可观测时空混沌系统的无模型预测
Unsupervised Mixture Estimation via Approximate Maximum Likelihood based on the Cramér - von Mises distance
论文作者
论文摘要
具有动态权重的混合物分布是建模损失数据的有效方法，其特征是重尾。但是，该模型家族的最大似然估计很困难，主要是因为需要在数值上评估一个棘手的归一化常数。在这样的设置中，基于仿真的估计方法是一种有吸引力的替代方法。采用大约最大似然估计（AMLE）方法。只要模拟是可行的，它是一种通用方法，可以应用于任何组件密度的混合物。重点放在动态对数正态征收的帕累托分布上，cramér -von mises距离用于测量观察到的样品和模拟样品之间的差异。在得出估计量的理论特性后，开发了一个混合程序，其中首先采用了标准的最大可能性来确定作为Amle所需的输入所需的统一先验的边界。仿真实验和两个真实数据应用表明，就标准最大似然估计而言，这种方法可取得重大改进。
Mixture distributions with dynamic weights are an efficient way of modeling loss data characterized by heavy tails. However, maximum likelihood estimation of this family of models is difficult, mostly because of the need to evaluate numerically an intractable normalizing constant. In such a setup, simulation-based estimation methods are an appealing alternative. The approximate maximum likelihood estimation (AMLE) approach is employed. It is a general method that can be applied to mixtures with any component densities, as long as simulation is feasible. The focus is on the dynamic lognormal-generalized Pareto distribution, and the Cramér - von Mises distance is used to measure the discrepancy between observed and simulated samples. After deriving the theoretical properties of the estimators, a hybrid procedure is developed, where standard maximum likelihood is first employed to determine the bounds of the uniform priors required as input for AMLE. Simulation experiments and two real-data applications suggest that this approach yields a major improvement with respect to standard maximum likelihood estimation.
