Topics in multivariate covariance estimation and time series analysis.

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dc.contributor.advisorHarvill, Jane L.
dc.contributor.authorBeeson, John D. (John David)
dc.contributor.departmentStatistical Sciences.en_US
dc.contributor.schoolsBaylor University. Dept. of Statistical Sciences.en_US
dc.date.accessioned2014-01-28T15:13:14Z
dc.date.available2014-01-28T15:13:14Z
dc.date.copyright2013-12
dc.date.issued2014-01-28
dc.description.abstractIn this dissertation we will discuss two topics relevant to statistical analysis. The first is a new test of linearity for a stationary time series, that extends the bootstrap methods of Berg et al. (2010) to goodness-of-fit (GoF) statistics specified in Harvill (1999) and Jahan and Harvill (2008). Berg's bootstrap method utilizes the statistics specified in Hinich (1982) in the framework of an autoregressive bootstrap procedure, however we show that by utilizing GoF methods, we can increase the power of the test. In Chapter three we discuss an alternative way of approaching the Friedman (1989) regularized discriminant method. Regularized discriminant analysis (RDA) is a well-known method of covariance regularization for the multivariate-normal based discriminant function. RDA generalizes the ideas of linear (LDA), quadratic (QDA), and mean-eigenvalue covariance regularization methods into one framework. The original idea and known extensions involve cross-validating in potentially high di- mensions, and can be highly computational. We propose using the Kullback-Leibler divergence as an optimization method to estimate a linear combination of class co- variance structures, which increases the accuracy of the RDA method, an limits the use of leave one out cross validation.en_US
dc.description.degreePh.D.en_US
dc.identifier.urihttp://hdl.handle.net/2104/8896
dc.language.isoen_USen_US
dc.publisheren
dc.rightsBaylor University theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact librarywebmaster@baylor.edu for inquiries about permission.en_US
dc.rights.accessrightsWorldwide access.en_US
dc.rights.accessrightsAccess changed 5/31/16.
dc.subjectStatistics.en_US
dc.subjectStatistical hypothesis testing.en_US
dc.subjectMultivariate analysisen_US
dc.titleTopics in multivariate covariance estimation and time series analysis.en_US
dc.typeThesisen_US

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