Nonparametric Fusion Learning for Multiparameters: Synthesize Inferences From Diverse Sources Using Data Depth and Confidence Distribution
Nonparametric Fusion Learning for Multiparameters: Synthesize Inferences From Diverse Sources Using Data Depth and Confidence Distribution
复制标题
多参数的非参数融合学习：使用数据深度和置信分布从不同来源综合推论
DOI：
10.1080/01621459.2021.1902817
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发表时间：
2021
影响因子：
3.7
通讯作者：
Xie, Min-ge
中科院分区：
文献类型：
--
作者：
Liu, Dungang;Liu, Regina Y.;Xie, Min-ge
融合学习是指综合来自多个来源或研究的推断，以做出比任何单独来源或研究更有效的推断和预测。大多数现有的合成推理方法依赖于参数模型假设，如正态性，这在实践中往往不成立。我们提出了一个通用的非参数融合学习框架，用于合成来自不同研究的多参数推断。该框架的主要工具是深度置信度分布（depth-CD）的新概念，它是由数据深度和置信度分布相结合而发展起来的。一般来说，深度CD是目标参数的可用推断信息的数据驱动的非参数汇总分布。我们表明，深度CD是一个强大的推理工具，而且，是一个综合形式的置信区域，其轮廓的水平集收缩向真正的参数值。提出的融合学习方法结合了个体研究的深度CD，每个深度CD由非参数引导和数据深度构建。该方法被证明是有效的，一般androbust。具体而言，它实现了高阶精度和Bahadur效率下适当选择的组合元素。它允许模型或推理结构在各个研究中有所不同。而且，它很容易适应具有广泛复杂和不规则设置的异质研究。最后一个属性使该方法能够使用来自不完整研究的间接证据来获得整体推理的效率。我们开发的理论支持所提出的方法，我们也说明了该方法在联合推断的共同均值向量和相关系数从几个研究。数值模拟结果表明，在非正态背景下，该方法比传统方法具有更小的偏差和更高的效率。该方法的优点也在联邦航空管理局的飞机着陆性能研究中得到了证明。本文的补充材料可在网上查阅。
Fusion learning refers to synthesizing inferences from multiple sources or studies to make a more effective inference and prediction than from any individual source or study alone. Most existing methods for synthesizing inferences rely on parametric model assumptions, such as normality, which often do not hold in practice. We propose a general nonparametric fusion learning framework for synthesizing inferences for multiparameters from different studies. The main tool underlying the proposed framework is the new notion ofdepth confidence distribution (depth-CD), which is developed by combining data depth and confidence distribution. Broadly speaking, adepth-CDis a data-driven nonparametric summary distribution of the available inferential information for a target parameter. We show that adepth-CDis a powerful inferential tool and, moreover, is an omnibus form of confidence regions, whose contours of level sets shrink toward the true parameter value. The proposed fusion learning approach combinesdepth-CDs from the individual studies, with eachdepth-CDconstructed by nonparametric bootstrap and data depth. The approach is shown to beefficient,generalandrobust. Specifically, it achieves high-order accuracy and Bahadur efficiency under suitably chosen combining elements. It allows the model or inference structure to be different among individual studies. And, it readily adapts to heterogeneous studies with a broad range of complex and irregular settings. This last property enables the approach to use indirect evidence from incomplete studies to gain efficiency for the overall inference. We develop the theoretical support for the proposed approach, and we also illustrate the approach in making combined inference for the common mean vector and correlation coefficient from several studies. The numerical results from simulated studies show the approach to be less biased and more efficient than the traditional approaches in nonnormal settings. The advantages of the approach are also demonstrated in aFederal Aviation Administrationstudy of aircraft landing performance. Supplementary materials for this article are available online.
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