Date of Award

2017

Document Type

Open Access Dissertation

Department

Statistics

Sub-Department

College of Arts and Sciences

First Advisor

Joshua M. Tebbs

Second Advisor

Dewei Wang

Abstract

Ordering and dependency are two aspects to describe the relationship between two random variables. In this thesis, we choose two hypothesis testing problems to tackle; i.e., a goodness-of-fit test for uniform stochastic ordering and one for positive quadrant dependence. For the test for uniform stochastic ordering, we propose new nonparametric tests based on ordinal dominance curves. We derive the limiting distributions of test statistics and provide the least favorable configuration to determine critical values. Numerical evidence is presented to support our theoretical results, and we apply our methods to a real data set. An extension for random right-censored data is provided. For the test for positive quadrant dependence, we propose empiricallikelihood- based testing approaches. Without the need to estimate or smooth distribution or copula functions, our proposed testing procedure is more straightforward than previous methods. Simulation results show that our proposed tests are competitive in realistic settings. Stock price data sets are provided for illustration. An extension to test for exchangeability is provided.

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