Model-free methods for multiple testing and predictive inference

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Recent advances in technology have allowed us to collect, store and process an enormous amount of data, bringing unprecedented challenges to interpretable data analysis: first, the structure of data is often complicated, while model assumptions are hard to justify in practice; second, the algorithms used to analyze the data can be extremely complex---think of the convolutional neural nets---making it difficult to develop validity guarantees for the results. Indeed, it has been noticed by researchers that many of the classical statistical methods fail when applied to the modern type of problems---we need a new set of tools to conduct statistical data analysis in the modern era. This dissertation contributes to the toolbox of statistical data analysis in the modern world by presenting several model-free methods for multiple testing and predictive inference. The methods proposed in this dissertation, building upon knockoffs and conformal inference, bypass the modelling of the data structure and the analysis of complex algorithms, and work as wrappers of other (potentially black-box) existing algorithms. Despite the flexibility of these methods, they are guaranteed to achieve statistical validity under the minimal set of assumptions. The validity and efficacy of these methods are evaluated in extensive numerical experiments. Applying these methods to real genetic and clinical data has led to new scientific insights.


Type of resource text
Form electronic resource; remote; computer; online resource
Extent 1 online resource.
Place California
Place [Stanford, California]
Publisher [Stanford University]
Copyright date 2021; ©2021
Publication date 2021; 2021
Issuance monographic
Language English


Author Ren, Zhimei
Degree supervisor Candès, Emmanuel J. (Emmanuel Jean)
Thesis advisor Candès, Emmanuel J. (Emmanuel Jean)
Thesis advisor Owen, Art B
Thesis advisor Tibshirani, Robert
Degree committee member Owen, Art B
Degree committee member Tibshirani, Robert
Associated with Stanford University, Department of Statistics


Genre Theses
Genre Text

Bibliographic information

Statement of responsibility Zhimei Ren.
Note Submitted to the Department of Statistics.
Thesis Thesis Ph.D. Stanford University 2021.

Access conditions

© 2021 by Zhimei Ren
This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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