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Spectral-based tests for periodicities

Wei, Lai
http://rave.ohiolink.edu/etdc/view?acc_num=osu1201706810

Abstract Details

2008, Doctor of Philosophy, Ohio State University, Statistics.
In this thesis, tests for periodicity are investigated based on a spectral analysis of a time series. Some important fundamental theories of spectral analysis of stationary and harmonic processes are reviewed. A regression model is developed in the frequency domain based on the Fourier transformation. We present some of the periodogram based tests, which are the global test and three local tests, i.e., the hearing test, local F test and Thomson's multitaper test. We will show that most of the tests can be derived from our regression model with the error term having an approximately diagonal covariance matrix. The distribution of the error term of the spectral regression model is based on the asymptotic distribution of the tapered Fourier transform of the error process. This asymptotic distribution has approximately a diagonal covariance matrix when the sample size is large and the spectral density functions (SDFs) of error processes have small dynamic range. Standard global tests for periodicity are often based on the assumption of a Gaussian IID error process. Using a smoothing spline approach, we extend the global test to the non-IID case. We contrast the F test in the time domain and the local F test in the frequency domain as well as the global and local spectral-based tests. Using regression-based F tests, we demonstrate that asymptotic size and power calculations can be made for some of these tests. We compare the size and power at finite sample sizes, under a number of different experimental conditions. According to the exploratory data analysis, we applied the local F test to Distortion Product Otoacoustic Emissions (DPOAEs), collected in the Department of Speech and Hearing Sciences, OSU. The logistic regression model and the noncentral F mixed effects regression models are explored to capture the important features of hearing data. In particular, noncentral-F mixed effects regression models capture within-subject-variability of the distortion products of healthy hearing subjects. The Penalized Quasi-Likelihood method is used to estimate the model parameters and we demonstrate how to do the model selection and diagnosing.
Peter Craigmile (Advisor)
167 p.
Statistics
Harmonic processes; Global and local spectral tests; Tapering; ; Maximum likelihood; Quasi-likelihood; Distortion product otoacoustic emissions; ; Noncentral-F mixed-effects model

Recommended Citations

Citations

  • Wei, L. (2008). Spectral-based tests for periodicities [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1201706810

    APA Style (7th edition)

  • Wei, Lai. Spectral-based tests for periodicities. 2008. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1201706810.

    MLA Style (8th edition)

  • Wei, Lai. "Spectral-based tests for periodicities." Doctoral dissertation, Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1201706810

    Chicago Manual of Style (17th edition)

osu1201706810
1,667
© 2008, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.