Tests of Bivariate Stochastic Order

• Main Author: Liu, Yunfeng
• Other Authors: Ivanoff, Gail
• Language: en
• Published: Université d'Ottawa / University of Ottawa 2011
• Subjects: bivariate stochastic order; Kendall statistic; Spearman statistic; bivariate Mann Whitney Wilcoxon statistic
• Online Access: http://hdl.handle.net/10393/20257; http://dx.doi.org/10.20381/ruor-4850

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.