Inference for the Bilaterally Contaminated Normal Model with Nuisance Parameter

• Activity Number: 323
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: SSC
• Author(s): Richard Charnigo*+ and Qian Fan and Douglas Bittel and Hongying Dai
• Companies: University of Kentucky and University of Kentucky and Children's Mercy Hospital and Children's Mercy Hospital
• Keywords: mixture ; contamination ; microarray ; gene expression ; large scale hypothesis testing

Abstract

Consider a three-component normal mixture model such that: (i) one component mean is assumed to equal zero; (ii) the other two component means are assumed nonnegative and nonpositive respectively but otherwise unknown; and, (iii) the component variances are assumed equal but otherwise unknown. This model, called the "bilaterally contaminated normal model with nuisance parameter" may be used to describe a large collection of Z statistics arising from a microarray experiment, with positive Z statistics corresponding to gene overexpression and negative Z statistics corresponding to gene underexpression. In this work we explore how to test the null hypothesis that the bilaterally contaminated normal model with nuisance parameter can be reduced to a single normal distribution with mean zero (no systematic overexpression or underexpression in a microarray context) and how to test the null hypothesis of reduction to a unilaterally contaminated normal model (systematic overexpression but not underexpression, or vice versa). An illustrative example involving a real microarray data set is featured.