A Two-Sample Test for Equality of Means in High Dimension.
We develop a test statistic 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 HotellingT2test. The proposed procedure, called the generalized component test, avoids full estimation of the covariance matrix by assuming that thepcomponents admit a logical ordering such that the dependence between components is related to their displacement. The test is shown to be competitive with other recently developed methods under ARMA and long-range dependence structures and to achieve superior power for heavy-tailed data. The test does not assume equality of covariance matrices between the two populations, is robust to heteroscedasticity in the component variances, and requires very little computation time, which allows its use in settings with very largep. An analysis of mitochondrial calcium concentration in mouse cardiac muscles over time and of copy number variations in a glioblastoma multiforme data set from The Cancer Genome Atlas are carried out to illustrate the test.
Department of Statistics, Texas A&M University, 3143 TAMU, College Station, TX 77843-3143 kbgregory@stat.tamu.edu.
Karl Bruce
KB
Gregory
Department of Statistics, Texas A&M University, 3143 TAMU, College Station, TX 77843-3143 carroll@stat.tamu.edu.
Raymond J
RJ
Carroll
Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, TX, 77230-1402, USA veera@mdanderson.org.
Veerabhadran
V
Baladandayuthapani
Department of Statistics, North Carolina State University, 2311 Stinson Drive, Raleigh, NC 27695-8203 snlahiri@ncsu.edu.
Soumendra N
SN
Lahiri
copy number variation; heteroscedasticity; large p; two-sample