LE3 .A278 2014

2014

Zhang, Ying
Cabilio, Paul

Acadia University

Degree of Master of Science

Masters

Mathematics and Statistics

Mathematics & Statistics

In health policy research, we are interested in determining if there is a sig- ni cant change in the behaviour of prescribing physicians pre- and post-policy change. Because such data are dependent, typical methods for con dence inter- val construction do not necessarily apply. The current methods assume that the data follow an independent process, and rely on the variance of that process. In this thesis we use properties of the sign and Wilcoxon signed rank statistics to construct con dence intervals when the data are dependent, and compare the two methods. Speci cally, we use the theory of U-statistics to develop asymptotic nor- mality theorems for these statistics, which are then used for con dence interval construction. The variances of the sign and Wilcoxon signed rank statistics are key in computing the con dence intervals. We consider both the unrealistic case in which we know the distribution from which the sample was drawn and are able to compute the variances exactly, and the more realistic situation in which the variance must be estimated due to lack of information. We use block and sieve bootstrapping methods for variance estimation, as well as an empirical distribu- tion method. Finally, these methods are applied to a real data set provided by the Nova Scotia Health Research Foundation.

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https://scholar.acadiau.ca/islandora/object/theses:308