Simulation-Based Hypothesis Testing of High Dimensional Means Under Covariance Heterogeneity

In this paper, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to compute the critical values. Different from the existing tests that heavily rely on the structural conditions on the unknown covariance matrices, the proposed tests allow general covariance structures of the data and therefore enjoy wide scope of applicability in practice. To enhance powers of the tests against sparse alternatives, we further propose two-step procedures with a preliminary feature screening step. Theoretical properties of the proposed tests are investigated. Through extensive numerical experiments on synthetic datasets and an human acute lymphoblastic leukemia gene expression dataset, we illustrate the performance of the new tests and how they may provide assistance on detecting disease-associated gene-sets. The proposed methods have been implemented in an R-package HDtest and are available on CRAN.Comment: 34 pages, 10 figures; Accepted for biometric

QCD Radiative Correction to the Hadronic Annihilation Rate of 1+−1^{+-} Heavy Quarkonium

Hadronic annihilation rate of $1^{+-}$ heavy quarkonium is given to next-to-leading order in $\alpha_s$ and leading order in $v^2$ using a recently developed factorization formalism which is based on NRQCD. The result includes both the annihilation of P-wave color-singlet $Q\bar{Q}$ component, and the annihilation of S-wave color-octet $Q\bar{Q}$ component of the quarkonium. The notorious infrared divergences due to soft gluons, i.e., the Logarithms associated with the binding energy, encountered in previous perturbative calculations of $1^{+-}$ quarkonium decays are found to be explicitly cancelled, and a finite result for the decay width to order $\alpha_s^3$ is then obtained.Comment: 15 pages latex (6 figures included). In this revised version a update reference and acknowledgement are include