NORMAL MIXTURE AND CONTAMINATED MODEL WITH NUISANCE PARAMETER AND APPLICATIONS

• Main Author: Fan, Qian
• Format: Others
• Published: UKnowledge 2014
• Subjects: bilaterally contaminated normal model; UnionIntersection test; hierarchical normal mixture model; singular Bayesian information criterion; singular flexible information criterion; Microarrays; Multivariate Analysis; Statistical Methodology; Statistical Models
• Online Access: http://uknowledge.uky.edu/statistics_etds/9; http://uknowledge.uky.edu/cgi/viewcontent.cgi?article=1011&context=statistics_etds

This paper intend to find the proper hypothesis and test statistic for testing existence of bilaterally contamination when there exists nuisance parameter. The test statistic is based on method of moments estimators. Union-Intersection test is used for testing if the distribution of population can be implemented by a bilaterally contaminated normal model with unknown variance. This paper also developed a hierarchical normal mixture model (HNM) and applied it to birth weight data. EM algorithm is employed for parameter estimation and a singular Bayesian information criterion (sBIC) is applied to choose the number components. We also proposed a singular flexible information criterion which in addition involves a data-driven penalty.