Kelly, Ryan
(2020)
Distribution Free Prediction Intervals for Multiple Functional Regression.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
My research aims to establish a method of constructing prediction intervals for a scalar response of interest when predictors are functional data, with minimal distributional and modeling assumptions. To accommodate flexible regression relationships, we integrated nonparametric functional regression based on functional principal component analysis into our conformal prediction method, and we developed nonparametric functional regression approaches based on the signature method, which is a mathematical tool to represent the information contained in the functions by a collection of iterated integrals. The prediction intervals constructed by the conformal method have guaranteed coverage (confidence) without the heavy restrictions on the error distribution and on the regression function, while the efficiency (implied by the length of the intervals) will depend on the representation and information compression of the functional predictors. Conditions necessary for efficiency and contiguity of the prediction set are discussed. Finally, our methods are illustrated using simulated and real data examples.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
|
| Date: |
16 September 2020 |
| Date Type: |
Publication |
| Defense Date: |
31 July 2020 |
| Approval Date: |
16 September 2020 |
| Submission Date: |
31 July 2020 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
74 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Statistics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Multiple Functional Regression, Prediction Intervals, Conformal Prediciii
tion, Multiple Functional Principal Components Analysis, Signature Expansion. |
| Date Deposited: |
16 Sep 2020 14:13 |
| Last Modified: |
16 Sep 2020 14:13 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/39495 |
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