Topics in selective inference and its application to instrumental variables
Abstract/Contents
- Abstract
- This thesis addresses problems in statistical inference after model selection procedures. The framework we adopt throughout the discussion is selective inference, which provides with valid inference conditioning on the model selection event. Chapter 1 gives a background introduction to the problem of interest and the guiding principle of selective inference, especially inference with randomization. Chapter 2 introduces the framework of inferactive data analysis, so-named to emphasize on inference after interactive data analysis. Chapter 3 discusses the problem of valid inference for the treatment effect after selecting invalid instrumental variables via a data-driven Lasso type selection procedure called SisVive. Instrumental variables models are widely used in Economics as well as Mendelian randomization in Genetics, and our method would be helpful for the practical use of instrument variables when it is not certain whether they are all valid or not. Our approach is conditional inference via selective inference with randomization, and fits into the general data analysis framework discussed in Chapter 2. We demonstrate the inference method through a development economics dataset and also a Mendelian randomization dataset with only summary statistics. Chapter 4 discusses the problem of valid inference for the treatment effect after pre-testing the strengths of instrumental variables via an F test. This is a widely used screening step in practical instrument variables data analysis, and people would only proceed to conduct inference and report results if the dataset passed the pre-test. We will show the common practice of ignoring the selection effect could result in significant bias in certain scenarios, while our inference method will correct for it. Again we adopt the conditional inference approach and demonstrate the method through two educational economics datasets.
Description
| 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 | 2019; ©2019 |
| Publication date | 2019; 2019 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Bi, Nan |
|---|---|
| Degree supervisor | Taylor, Jonathan E |
| Thesis advisor | Taylor, Jonathan E |
| Thesis advisor | Lai, T. L |
| Thesis advisor | Tibshirani, Robert |
| Degree committee member | Lai, T. L |
| Degree committee member | Tibshirani, Robert |
| Associated with | Stanford University, Department of Statistics. |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Nan Bi. |
|---|---|
| Note | Submitted to the Department of Statistics. |
| Thesis | Thesis Ph.D. Stanford University 2019. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2019 by Nan Bi
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