论文标题
统一的可再生加权款项规则，用于各种在线更新估算
Unified Rules of Renewable Weighted Sums for Various Online Updating Estimations
论文作者
论文摘要
本文建立了可再生加权总和（RW）的统一框架，用于使用流数据集的模型中的各种在线更新估计。新定义的RWS奠定了在线更新可能性，在线更新损失功能，在线更新估计方程等的基础。 RWS的想法是直观和启发式的，并且该算法在计算上很简单。本文选择非参数模型作为示例性设置。 RWS适用于各种类型的非参数估计量，其中包括但不限于非参数可能性，准类和最小二乘。此外，该方法和理论可以扩展到具有参数和非参数函数的模型中。建立了拟议的可再生估计量的估计一致性和渐近正态性，并获得了Oracle属性。此外，这些属性始终得到满足，没有对数据批次数量的任何限制，这意味着新方法适应了流媒体数据集永久到达的情况。通过模拟实验和实际数据分析的各种数值示例进一步说明了该方法的行为。
This paper establishes unified frameworks of renewable weighted sums (RWS) for various online updating estimations in the models with streaming data sets. The newly defined RWS lays the foundation of online updating likelihood, online updating loss function, online updating estimating equation and so on. The idea of RWS is intuitive and heuristic, and the algorithm is computationally simple. This paper chooses nonparametric model as an exemplary setting. The RWS applies to various types of nonparametric estimators, which include but are not limited to nonparametric likelihood, quasi-likelihood and least squares. Furthermore, the method and the theory can be extended into the models with both parameter and nonparametric function. The estimation consistency and asymptotic normality of the proposed renewable estimator are established, and the oracle property is obtained. Moreover, these properties are always satisfied, without any constraint on the number of data batches, which means that the new method is adaptive to the situation where streaming data sets arrive perpetually. The behavior of the method is further illustrated by various numerical examples from simulation experiments and real data analysis.
