The purpose of this thesis is to compare rank-based tests of bivariate stochastic order. Given two bivariate distributions $F$ and $G$, the general problem we are dealing with is to test $H_0: F=G$ against $H_1:F<G$, where $F$ and $G$ are independent continuous distributions on $\Re ^2$. (``$F<G$" means that $F(x)\leq G(x)~\forall x\in \Re^2$, and $\exists x\in \Re^2$ such that $F(x)< G(x)$.). In particular, we will analyze three analogues of the one-dimensional Mann-Whitney-Wilcoxon test in two dimensions. Two of the test statistics are new; we call them the Kendall and Spearman statistics. We will then show the asymptotic distributions and carry out empirical comparisons of the Kendall, Spearman and the third two-dimensional Mann-Whitney-Wilcoxon statistics.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/20257 |
| Date | January 2011 |
| Creators | Liu, Yunfeng |
| Contributors | Ivanoff, Gail |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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