This thesis considers the problem of hypothesis testing for umbrella alternatives when there are two groups, or strata, of observations. The proposed methods extend a previously established general framework of hypothesis testing based on rankings to stratified datasets by first aligning the strata. The tests based on the Spearman and Kendall distances between ranking vectors lead to the traditional aligned-rank tests and new methods which account for “misalignment” under the alternative hypothesis. Asymptotic null distributions and simulation studies are given for the Spearman distance. Diagnostic tools for the misalignment issue are illustrated alongside the proposed tests on a dataset of IQ scores of coma patients. Extensions to three or more strata and ”adaptive” tests are provided as future research directions.

abstract: With the increase in computing power and availability of data, there has never been a greater need to understand data and make decisions from it. Traditional statistical techniques may not be adequate to handle the size of today's data or the complexities of the information hidden within the data. Thus knowledge discovery by machine learning techniques is necessary if we want to better understand information from data. In this dissertation, we explore the topics of asymmetric loss and asymmetric data in machine learning and propose new algorithms as solutions to some of the problems in these topics. We also studied variable selection of matched data sets and proposed a solution when there is non-linearity in the matched data. The research is divided into three parts. The first part addresses the problem of asymmetric loss. A proposed asymmetric support vector machine (aSVM) is used to predict specific classes with high accuracy. aSVM was shown to produce higher precision than a regular SVM. The second part addresses asymmetric data sets where variables are only predictive for a subset of the predictor classes. Asymmetric Random Forest (ARF) was proposed to detect these kinds of variables. The third part explores variable selection for matched data sets. Matched Random Forest (MRF) was proposed to find variables that are able to distinguish case and control without the restrictions that exists in linear models. MRF detects variables that are able to distinguish case and control even in the presence of interaction and qualitative variables. / Dissertation/Thesis / Ph.D. Industrial Engineering 2013