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theses

In this dissertation, we develop new methods for problems for the two fundamental topics of statistical learning - inference and prediction, using the tool of confidence distribution (CD). Specifically, we are interested in i) making efficient and valid statistical inference about an individual subject, by borrowing information from other individual subjects with similar traits, in a heterogeneous database that contains many individual subjects, and ii) effectively and accurately quantifying uncertainties associated with the prediction of future observations from a model estimated based on past observations. For the first problem, we propose an individualized fusion learning (iFusion) approach, for drawing efficient individualized inference by fusing information from relevant data sources. iFusion is robust for handling heterogeneity arising from diverse sources, and is ideally suited for goal-directed applications such as precision medicine. Specifically, iFusion summarizes individual inferences as CDs, then adaptively forms a clique of individuals that bears relevance to the target individual, and finally combines the CDs from those relevant individuals and draws inference for the target individual based on it. In essence, iFusion “borrows strength” from relevant individuals to improve inference efficiency while retaining inference validity. Computationally, it is parallel in nature and scales up well in comparison with its competitors such as many of the Bayesian methods. Examples in simulations and a real application in financial forecasting are further presented to demonstrate the effectiveness of iFusion. For the second problem, a general prediction framework is proposed in which prediction is presented in the form of a predictive distribution function. This predictive distribution function is well suited for the notion of confidence subscribed in the frequentist interpretation, and can provide meaningful answers for questions related to prediction. A general approach under this framework is formulated and illustrated by using the concept of CD. This CD-based prediction approach inherits many desirable properties of CD, including its capacity for serving as a common platform for connecting and unifying the existing procedures of predictive inference in Bayesian, fiducial and frequentist paradigms. The theory underlying the CD-based predictive distribution is developed and some related efficiency and optimality issues are addressed. Moreover, a simple yet broadly applicable Monte-Carlo algorithm is proposed for the implementation of the proposed approach. This concrete algorithm together with the proposed definition and associate theoretical development produces a comprehensive statistical inference framework for prediction. Finally, the approach is applied to simulation studies, and a real project on predicting the incoming volume of application submissions to a government agency. The latter shows the applicability of the proposed approach to dependent data settings.

ETD_8432

Ph.D.

Includes bibliographical references

by Jieli Shen

doi:10.7282/T3KS6VQB

ETD doctoral

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