15,620 research outputs found
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 Heavy Quarkonium
Hadronic annihilation rate of heavy quarkonium is given to
next-to-leading order in and leading order in using a recently
developed factorization formalism which is based on NRQCD. The result includes
both the annihilation of P-wave color-singlet component, and the
annihilation of S-wave color-octet 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 quarkonium decays are found to be explicitly
cancelled, and a finite result for the decay width to order is
then obtained.Comment: 15 pages latex (6 figures included). In this revised version a update
reference and acknowledgement are include
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