A0486
Title: Nonparametric fusion learning using confidence distribution, data depth and bootstrap
Authors: Dungang Liu - University of Cincinnati (United States) [presenting]
Regina Liu - Rutgers University (United States)
Min-ge Xie - Rutgers University (United States)
Abstract: Fusion learning refers to synthesize inferences from diverse sources to provide more effective inference than any individual source. Commonly used methods rely on parametric model assumptions, such as the normality, which may not hold in practice. We propose a general nonparametric framework for fusion learning. The framework enables us to synthesize inferences of a set of target population parameters of interest in a nonparametric manner, i.e., without requiring any distribution specification. The key notion used in our development is the depth confidence distribution (CD), a summary of inferential information for the target parameters. We demonstrate that a depth CD is a useful inferential tool in the sense that it is an omnibus form of confidence regions and p-values, and its contours shrink to the true parameter values. To achieve nonparametric learning, we propose a fusion of depth CDs derived by nonparametric bootstrap in each study. This method can achieve high-order accuracy and Bahadur efficiency by specifying certain combining elements. It can also adapt to complex and irregular settings where the studies are heterogeneous. The advantages of our fusion method are also illustrated in a study of aircraft landings.
