Rothenberger, Scott D.
(2015)
Analysis of Functional Correlations.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
Technological advances have led to an increase in the collection of high-dimensional, nearly continuously sampled signals. Evolutionary correlations between such signals are salient to many studies, as they provide important information about associations between different dynamic processes and can be used to understand how these processes relate to larger complex mechanisms. Despite the large number of methods for analyzing functional data that have been explored in the past twenty-five years, there is a dearth of methods for analyzing functional correlations. This dissertation introduces new methods for addressing three questions pertaining to functional correlations. First, we address the problem of estimating a single functional correlation by developing a smoothing spline estimator and accompanying bootstrap procedure for forming confidence intervals. Next, we consider the problem of testing the equivalence of two functional correlations from independent samples by developing a novel adaptive Neyman testing procedure. Lastly, we address the problem of testing the equivalence of two functional correlations from dependent samples by extending the adaptive Neyman test to this more complicated setting, and by embedding the problem in a state-space framework to formulate a practical Kalman filter-based algorithm for its implementation. These methods are motivated by questions in sleep medicine and chronobiology and are used to analyze the dynamic coupling between delta EEG power and high frequency heart rate variability during sleep.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
| Creators | Email | Pitt Username | ORCID  |
|---|
| Rothenberger, Scott D. | sdr49@pitt.edu | SDR49 | |
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| ETD Committee: |
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| Date: |
14 January 2015 |
| Date Type: |
Publication |
| Defense Date: |
20 November 2014 |
| Approval Date: |
14 January 2015 |
| Submission Date: |
4 December 2014 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
78 |
| 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: |
functional data analysis, functional correlation, adaptive Neyman test, smoothing spline, electroencephalography, heart rate variability |
| Date Deposited: |
14 Jan 2015 15:46 |
| Last Modified: |
19 Dec 2016 14:42 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/23784 |
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