Conference on Robust Rank-Based and Nonparametric Methods
April 10 (Fri) 10:30 a.m.

Effective Fusion Learning: Combining Inferences from Multiple Studies Using Data Depth, Bootstrap and Confidence Distributions

Regina Liu
Department of Statistics
Rutgers University

Learning from multiple studies can often be fused together to yield to a more effective overall inference than individual studies alone. Such effective fusion learning is of vital importance, especially in light of the trove of data nowadays collected routinely from various sources in all domains and at all time.

Using a project of tracking aircraft landing performance as an illustrative example, we present an effective fusion learning approach. Specifically, we apply the concept of confidence distribution (CD) and data depth together with bootstrap to develop a new nonparametric approach for combining inferences from multiple studies for a common hypothesis. A CD is a sample-dependent distribution function that can be used to estimate an unknown parameter. It can be viewed as a "distribution estimator" (rather than the usual point or interval estimator) of the parameter. CD has been shown to be effective tools in statistical inference. Examples of CD include bootstrap distribution and significance function (also referred to as p-value function). We discuss a new nonparametric approach to combining test results from independent studies. Specifically, in each study we apply data depth and bootstraps to obtain a p-value function for the common hypothesis. The p-value functions are then combined under the framework of combining CDs. This approach is completely data driven and shown to have several advantages, in theory and implementation. The proposed approach provides a valid inference approach for a broad class of testing problems involving multiple studies where the parameters of interest can be either finite or infinite dimensional, and the tests used in individual studies may vary. Illustrations using simulation data and aircraft landing data collected from airlines will be presented.

This is joint work with Dungang Liu (Yale University) and Minge Xie (Rutgers University).



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