Topics in causal and high dimensional inference
- Causality is a central concept in science and philosophy. With the ever increasing amount and complexity of data being collected, statistics is playing a more and more significant role in the inference of causes and effects. This thesis consists of three Parts. Part I reviews the necessary mathematical languages so we can talk about causality. Three major approaches (by potential outcomes in Chapter 2, by graphs in Chapter 3, and by functions in Chapter 4) are described. They are in many senses equivalent or complementary to each other, and excel in different causal tasks. Part II considers the statistical inference of a single causal effect in the potential outcome framework. Chapter 5 reviews state-of-the-art matching and weighting methods. Chapter 6 proposes a new loss function tailored for propensity score estimation, which can boost the performance of the weighting methods. Chapter 7 reviews outcome regression and doubly robust inference and provides some insight to selecting propensity score models and constructing confidence intervals. Part III considers the statistical inference of multiple confounded effects. Chapter 8 introduces a confounding problem in linear model with latent variables. Two examples are given, one in genetics and one in finance. Chapter 9 proposes a twp-step procedure to adjust for the hidden confounding variables in high dimensional data. Chapter 10 presents the performance of this method in simulations and the two read data examples.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Stanford University, Department of Statistics.
|Owen, Art B
|Owen, Art B
|Statement of responsibility
|Submitted to the Department of Statistics.
|Thesis (Ph.D.)--Stanford University, 2016.
- © 2016 by Qingyuan Zhao
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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