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Analysis of Functional Correlations

Rothenberger, Scott D. (2015) Analysis of Functional Correlations. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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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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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Rothenberger, Scott D.sdr49@pitt.eduSDR49
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairIyengar, Satishssi@pitt.eduSSI
Committee CoChairKrafty, Robert
Committee MemberCheng, Yuyucheng@pitt.eduYUCHENG
Committee MemberJung, Sungkyusungkyu@pitt.eduSUNGKYU
Committee MemberHall, Marticahallmh@upmc.eduMHH1
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


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