High-dimensional inference and confidence sets of models
File(s)
Author(s)
Lewis, Rebecca
Type
Thesis
Abstract
In high-dimensional regression problems, a key aim is to identify a sparse model that fits
the data well. This may be used to form accurate predictions or to gain subject-matter
understanding. When strong dependence is present among covariates, it is common for
many models to fit the data equally well. Whilst it is sufficient to report a single model for
prediction, when the goal is to gain subject-matter understanding, Cox & Battey (2017)
argue that a confidence set of models – a set consisting of all models of appropriate fit
– should be reported and propose a method to achieve this aim. This thesis provides a
theoretical elucidation of this approach, and based on the results, explores further ideas
in high-dimensional data analysis.
the data well. This may be used to form accurate predictions or to gain subject-matter
understanding. When strong dependence is present among covariates, it is common for
many models to fit the data equally well. Whilst it is sufficient to report a single model for
prediction, when the goal is to gain subject-matter understanding, Cox & Battey (2017)
argue that a confidence set of models – a set consisting of all models of appropriate fit
– should be reported and propose a method to achieve this aim. This thesis provides a
theoretical elucidation of this approach, and based on the results, explores further ideas
in high-dimensional data analysis.
Version
Open Access
Date Issued
2023-05
Date Awarded
2023-08
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Battey, Heather
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)