The application of frequency domain methods to two statistical problems

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dc.contributor.advisor Prof. F Lombard en_US Potgieter, Gert Diedericks Johannes 2012-09-10T07:32:40Z 2012-09-10T07:32:40Z 2012-09-10 2001
dc.description D.Phil. en_US
dc.description.abstract We propose solutions to two statistical problems using the frequency domain approach to time series analysis. In both problems the data at hand can be described by the well known signal plus noise model. The first problem addressed is the estimation of the underlying variance of a process for the use in a Shewhart or CUSUM control chart when the mean of the process may be changing. We propose an estimator for the underlying variance based on the periodogram of the observed data. Such estimators have properties which make them superior to some estimators currently used in Statistical Quality Control. We also present a CUSUM chart for monitoring the variance which is based upon the periodogram-based estimator for the variance. The second problem, stimulated by a specific problem in Variable Star Astronomy, is to test whether or not the mean of a bivariate time series is constant over the span of observations. We consider two periodogram-based tests for constancy of the mean, derive their asymptotic distributions under the null hypothesis and under local alternatives and show how consistent estimators for the unknown parameters in the proposed model can be found en_US
dc.language.iso en en_US
dc.subject Statistical hypothesis testing - Asymptotic theory en_US
dc.subject CUSUM technique en_US
dc.subject Monte Carlo method en_US
dc.subject Statistical astronomy en_US
dc.subject Variable stars - Observations en_US
dc.title The application of frequency domain methods to two statistical problems en_US
dc.type Thesis en_US

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