Epsilon Open Archive

Abstract

In profile analysis, there exist three tests: test of parallelism, test of levels and test of flatness. In this thesis, these tests have been studied. Firstly, a classical setting, where the sample size is greater than the dimension of the parameter space, is considered. The hypotheses have been established and likelihood ratio tests have been derived. The distributions of these test statistics have been given. In the latter stage, all tests have been derived in a high-dimensional setting, where the number of parameters exceeds the number of sample size. Such settings have become more common due to the advances in computer technologies in the last decades. In high-dimensional data analysis, several issues arise with the dimensionality and different techniques have been developed to deal with these issues. We propose a dimension reduction method using scores that was first proposed by Läuter et al. (1996). To be able to find the specific distributions of the test statistics of profile analysis in this context, the properties of spherical distributions are utilized.