The numerical delta method, bootstrap, model selection, and parameter inference
Abstract/Contents
- Abstract
- The first chapter of this dissertation studies new inference methods for handling nondifferentiable functions of structural parameters. Such functions arise in many counterfactual analyses that policy makers use to assess the effectiveness of their policies. For example, a policy maker may want to determine for which individuals in a population a treatment is most effective. After estimating quantile treatment effects for several different quantiles, she wishes to provide standard errors for the maximum effect. The pointwise maximum function is nondifferentiable, which invalidates classical inference methods. In some cases, the function of interest may not even be directionally differentiable. In these cases, the directional delta method cannot be applied. Examples of functions that are not known to be directionally differentiable include many M-estimators with nondifferentiable objective functions, such as the maximum score estimator, the LASSO estimator, and the 1-norm Support Vector Machine (SVM) regression estimator. It is well established that the conventional bootstrap will not always consistently estimate the limiting distribution of these estimators and therefore cannot be used to conduct inference. As an alternative to the conventional bootstrap, the second chapter of this dissertation proposes a numerical bootstrap procedure which can consistently estimate the limiting distribution for a large class of estimators including those with convergence rates slower than root-n. Sometimes there are many different estimators policy makers can use to determine the effectiveness of their policies, and the question of how to select among the different estimators becomes important. The third chapter of this dissertation discusses how researchers can choose among the different estimators in a data-driven way and how to account for the variation in the estimate that arises from experimenting with different estimators. We propose to simulate the post selection distribution using subsampling by repeatedly performing model selection on each subsampled dataset and using the percentiles of the resulting subsampling distribution for inference.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2017 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Li, Jessie Q |
|---|---|
| Associated with | Stanford University, Department of Economics. |
| Primary advisor | Hong, Han |
| Thesis advisor | Hong, Han |
| Thesis advisor | Romano, Joseph P, 1960- |
| Thesis advisor | Wolak, Frank A |
| Advisor | Romano, Joseph P, 1960- |
| Advisor | Wolak, Frank A |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Jessie Q. Li. |
|---|---|
| Note | Submitted to the Department of Economics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2017. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2017 by Jessie Qianxi Li
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