A Two-Sample Test for Equality of Means in High Dimension

• Activity Number: 143
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Karl Gregory*+ and Soumendra N. Lahiri
• Companies: and North Carolina State University
• Keywords: two-sample test ; high dimensional ; large p ; small n ; copy number

Abstract

A test statistic is developed for testing the equality of two population mean vectors in the "large-p-small-n"setting. Such a test must surmount the rank-deficiency of the sample covariance matrix which breaks down the classic Hotelling T^2 test. The proposed procedure, called the generalized component test, avoids full estimation of the covariance matrix by assuming that the p components admit a logical ordering such that the dependence between two components is a function of their displacement. The test is shown to function well under ARMA and long-range dependence among the components, as well as under heteroscedasticity of the component variances, provided that component variances are not too close to zero. The method is demonstrated through simulation to be competitive with that of Chen and Qin (2010) in several settings as well as more powerful under heavy-tailedness and with heteroscedastic component variances. A real data example involving copy number data is given to illustrate the methodology.