Tests for constancy of the mean fall and rise times of a light curve

- Potgieter, Gert Diedericks Johannes

**Authors:**Potgieter, Gert Diedericks Johannes**Date:**2012-08-27**Subjects:**Stars , Light , Optics , Wave mechanics**Type:**Mini-Dissertation**Identifier:**uj:3162 , http://hdl.handle.net/10210/6579**Description:**M.Sc. , The brightness of many stars vary over time. A plot of the brightness against time is known as a light curve. The fall and rise times of the light curve can be modelled by two cross-correlated white noise processes. We propose four statistics to test the hypothesis of a constant mean fall and rise time of the light curve against the alternative that at least one of the fall or rise times exhibits a change in mean. The asymptotic null distributions of the test statistics are derived. The power of these four test statistics will be compared via Monte Carlo simulations for a few alternatives. The use of these test statistics is illustrated by application to data from the variable stars R Camelopardalis and R Cassiopeiae.**Full Text:**

**Authors:**Potgieter, Gert Diedericks Johannes**Date:**2012-08-27**Subjects:**Stars , Light , Optics , Wave mechanics**Type:**Mini-Dissertation**Identifier:**uj:3162 , http://hdl.handle.net/10210/6579**Description:**M.Sc. , The brightness of many stars vary over time. A plot of the brightness against time is known as a light curve. The fall and rise times of the light curve can be modelled by two cross-correlated white noise processes. We propose four statistics to test the hypothesis of a constant mean fall and rise time of the light curve against the alternative that at least one of the fall or rise times exhibits a change in mean. The asymptotic null distributions of the test statistics are derived. The power of these four test statistics will be compared via Monte Carlo simulations for a few alternatives. The use of these test statistics is illustrated by application to data from the variable stars R Camelopardalis and R Cassiopeiae.**Full Text:**

The application of frequency domain methods to two statistical problems

- Potgieter, Gert Diedericks Johannes

**Authors:**Potgieter, Gert Diedericks Johannes**Date:**2012-09-10**Subjects:**Statistical hypothesis testing - Asymptotic theory , CUSUM technique , Monte Carlo method , Statistical astronomy , Variable stars - Observations**Type:**Thesis**Identifier:**uj:9843 , http://hdl.handle.net/10210/7246**Description:**D.Phil. , 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**Full Text:**

**Authors:**Potgieter, Gert Diedericks Johannes**Date:**2012-09-10**Subjects:**Statistical hypothesis testing - Asymptotic theory , CUSUM technique , Monte Carlo method , Statistical astronomy , Variable stars - Observations**Type:**Thesis**Identifier:**uj:9843 , http://hdl.handle.net/10210/7246**Description:**D.Phil. , 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**Full Text:**

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