Publication Date


Document Type


First Advisor

Pourahmadi, Mohsen

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mathematical Sciences


Estimation theory; Statistical hypothesis testing; Sampling (Statistics)


Much research has been done recently on the application of the empirical characteristic function to various inference problems. In this thesis, new estimation and hypothesis testing procedures which are based on the empirical characteristic function are reviewed. The problem of selecting sampling times (of the empirical characteristic function) for some of these procedures is addressed, and algorithms for selecting these sampling times to ensure a powerful test are given. To investigate the power of some of these techniques, Monte Carlo studies are performed and the results presented. The empirical power of a symmetry test based on the empirical characteristic function using various methods of selecting sampling times is compared to that of the Wilcoxon symmetry test. These procedures are carried out for both small and large samples since the empirical characteristic function procedures rely on the asymptotic distribution of the test statistic. Some theoretical results concerning estimates used in the algorithm for selecting sampling times for the empirical characteristic function based procedures for bounded random variables are presented. These estimates are shown to be consistent and their distributions in terms of the population distribution are derived. It is also shown that the use of these estimates in selecting sampling times does not change the asymptotic distribution of the test statistic for the empirical characteristic function based hypothesis tests.


Bibliography: pages 36-38.


vi, 38 pages




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