Two sample test for high-dimensional partially paired data

In this paper, we study two sample test for the equality of mean vectors of high-dimensional partially paired data. Extending the results of Lim et al. [12], we propose a new type of regularized statistics, denoted by (Formula presented.) , which is a convex combination of the regularized Hotelling's t-statistic (HT) for two independent multivariate samples and that for multivariate paired samples. The proposed (Formula presented.) involves the shrinkage estimator of the covariance matrix and, depending on the choice of the shrinkage estimator, two versions of the (Formula presented.) are proposed. We compute the asymptotic null distribution of one version of the RT for a fixed tuning parameter of the covariance matrix estimation. A procedure to estimate the tuning parameter is proposed and discussed. The power of the proposed test is compared to two existing ad-hoc procedures, the HT based on a few principal components (PCs) from the PC analysis and that with the generalized inverse of the sample covariance matrix. It is also compared to the test with only independent two samples or paired samples. Finally, we illustrate the advantage of the (Formula presented.) using the microarray experiment of the liver cancer.

Duke Scholars

Author Sin-Ho Jung Biostatistics & Bioinformatics, Division of Integrative Geno ...