Computationally Intensive Methods for Spectrum Estimation

摘要

Spectrum estimation is an essential technique for analyzing time series data. A leading method in the field of spectrum estimation is the multitaper method. The multitaper method has been applied to many scientific fields and has led to the development of new methods for detection signals and modeling periodic data. Within these methods there are open problems concerning parameter selection, signal detection rates, and signal estimation. The focus of this thesis is to address these problems by using techniques from statistical learning theory. This thesis presents three theoretical contributions for improving methods related to the multitaper spectrum estimation method: (1) two hypothesis testing procedures for evaluating the choice of time-bandwidth, NW , and number of tapers, K, parameters for the multitaper method, (2) a bootstrapping procedure for improving the signal detection rates for the F-test for line components, and (3) cross-validation, boosting, and bootstrapping methods for improving the performance of the inverse Fourier transform periodic data estimation method resulting from the F-test. We additionally present two applied contributions: (1) a new atrial signal extraction method for electrocardiogram data, and (2) four new methods for analyzing, modeling, and reporting on hockey game play at the Major Junior level.