| The objective of this work is to suggest a new approach to statistical testing of stochastic dominance relations among random outcomes. More precisely, we test whether a random variable X is non-dominated by a random variable Y in the sense of stochastic dominance, assuming that their distributions are unknown. The approach is based on a recent analysis of mean-risk models and their consistence with stochastic dominance.; The comparison of probability distributions has been of considerable interest in various branches of science, finance, economics, insurance, medicine, etc. The stochastic dominance relation of second order is a very popular ordering relation due to the fact that it reflects risk-averse preferences. Stochastic dominance plays a fundamental role in the inequality and poverty analysis for comparison of income distributions, It has become increasingly important in optimization and decision making under uncertainty.; We present the concept of stochastic dominance, its basic properties, characterizations, necessary conditions, and implications. We discuss and compare several existing approaches for testing stochastic dominance, as well as present a novel one.; The dissertation consists of seven chapters. The first part of the dissertation provides fairly broad coverage of the literature on stochastic dominance inference. It contains the definitions of stochastic dominance, some aspects of the higher order stochastic dominance relations, properties, and implications. We provide an overview of statistical tests for stochastic dominance. Included are the hypothesis statements, assumptions, test statistics, power of the tests whenever such a study is available, as well as comments on the advantages and disadvantages of each test.; The second part of the dissertation contains the description of the new approach based on mean-risk inequalities. It facilitates tests of first, second and higher order stochastic dominance efficiency of a distribution. We suggest mean-risk statistics and show their consistency as estimators of the corresponding risk quantifiers in certain mean-risk models. Furthermore, we present a numerical study on several real-world data-sets and compare the outcome of our approach with other existing tests. Artificial data sets are used to study the power and the limitations of the new tests. |
