论文标题
单个数据和摘要统计数据的半参数有效融合
Semiparametric Efficient Fusion of Individual Data and Summary Statistics
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Suppose we have individual data from an internal study and various summary statistics from relevant external studies. External summary statistics have the potential to improve statistical inference for the internal population; however, it may lead to efficiency loss or bias if not used properly. We study the fusion of individual data and summary statistics in a semiparametric framework to investigate the efficient use of external summary statistics. Under a weak transportability assumption, we establish the semiparametric efficiency bound for estimating a general functional of the internal data distribution, which is no larger than that using only internal data and underpins the potential efficiency gain of integrating individual data and summary statistics. We propose a data-fused efficient estimator that achieves this efficiency bound. In addition, an adaptive fusion estimator is proposed to eliminate the bias of the original data-fused estimator when the transportability assumption fails. We establish the asymptotic oracle property of the adaptive fusion estimator. Simulations and application to a Helicobacter pylori infection dataset demonstrate the promising numerical performance of the proposed method.
