Publication Date

1985

Document Type

Dissertation/Thesis

First Advisor

Pourahmadi, Mohsen

Degree Name

M.S. (Master of Science)

Department

Department of Mathematical Sciences

LCSH

Estimation theory||Statistical hypothesis testing||Sampling (Statistics)

Abstract

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.

Comments

Bibliography: pages 36-38.

Extent

vi, 38 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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