Using the bootstrap to analyze variable stars data

Abstract

Often in statistics it is of interest to investigate whether or not a trend is significant. Methods for testing such a trend depend on the assumptions of the error terms such as whether the distribution is known and also if the error terms are independent. Likelihood ratio tests may be used if the distribution is known but in some instances one may not want to make such assumptions. In a time series, these errors will not always be independent. In this case, the error terms are often modelled by an autoregressive or moving average process. There are resampling techniques for testing the hypothesis of interest when the error terms are dependent, such as, modelbased bootstrapping and the wild bootstrap, but the error terms need to be whitened. In this dissertation, a bootstrap procedure is used to test the hypothesis of no trend for variable stars when the error structure assumes a particular form. In some cases, the bootstrap to be implemented is preferred over large sample tests in terms of the level of the test. The bootstrap procedure is able to correctly identify the underlying distribution which may not be χ2.