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Abstract:
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Fusion learning refers to synthesizing inferences from multiple studies to make better inference than from any individual study alone. We propose a general nonparametric fusion learning framework for synthesizing inferences of multi-parameters from different studies. The main tool is the new notion of depth confidence distribution (depth-CD), derived from combining data depth and confidence distributions. Broadly speaking, a depth-CD is a data-driven nonparametric summary distribution of the available inferential information for a target parameter. We show that a depth-CD is an omnibus form of confidence regions and an all-encompassing inferential tool. The proposed fusion learning approach combines depth-CDs from the individual studies, with each depth-CD devised from nonparametric bootstrap and data depth. The approach is efficient, general and robust. It achieves high-order accuracy and allows the models to be different among individual studies. It also readily adapts to a broad range of heterogeneous studies and is thus able to utilize indirect evidence to gain efficiency for the overall inference. The approach is illustrated in an aircraft landing performance study.
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