Nonparametric hypothesis testing for multivariate and complex data on sustainability

Abstract

The dissertation comprises three chapters, in which the whole thesis focuses on the nonparametric solution for hypothesis testing of multivariate and complex datasets. The complexity of the dataset includes in particular the violation of parametric assumptions, small sample size, one-sided alternative hypothesis, and missing data. In the second chapter, we review about permutation test for analyzing complex datasets. We attempt to figure out the limitation of the previous studies and suggest some possible remedies. In chapter 3, we study the power performance and asymptotic properties of the combined permutation test (CPT) for complex data. The simulation results reveal that the CPT is the only nonparametric solution to tackle the loss of degrees of freedom when the number of response variables is greater than the sample size. For the two-sample test, the most powerful CPT is based on the Tippett combination when the percentage of true partial alternative hypotheses is ≤30%, that based on the Fisher combination when the percentage is, >30% and <100%, and that based on the Liptak combination when the percentage is 100$\%$. Finally, we analyzed the multidimensional sustainable development goals in Ethiopia using CPT. Moreover, we advance the power behavior of the CPT for multivariate analysis of variance, especially for the ``big dataset". The simulation proves that the power of CPT increases as the number of samples and variables of the dataset increases. Besides, the proportion of true partial alternative hypotheses is more vital than the absolute number of variables in explaining the power improvement of CPT. Finally, we apply the CPT to study the organizational well-being of University workers. In chapter 4, we propose CPT for testing the significance of coefficients of the multivariate linear regression model. The simulation results prove that the proposed CPT is exact, unbiased, and consistent to test the significance of coefficients. The power of CPT increases as the number of dependent variables increases with fixed sample size. We applied the CPT to analyze multidimensional private firm performance in Ethiopia. Finally, chapter 5 consists of the summary of findings and future research work guidelines.