| In this dissertation, first we consider the problem of testing homogeneity and order in a contaminated normal model, when the data is correlated under some known covariance structure. To address this problem, we developed a moment based homogeneity and order test, and design weights for test statistics to increase power for homogeneity test. We applied our test to microarray about Down's syndrome data. This dissertation also studies a singular Bayesian information criterion (sBIC) for a bivariate hierarchical normal mixture model with varying weights, and develops a new data dependent information criterion (sFLIC). We apply our model and criteria to birthweight and gestational age data for the same model, whose purposes are to select model complexity from data.;KEYWORDS: Finite Mixture Models, Micro-array Analysis, Homogeneity Test, Information Criterion, Hierarchical Mixture Model. |
