276 research outputs found
Two-Sample Tests for High Dimensional Means with Thresholding and Data Transformation
We consider testing for two-sample means of high dimensional populations by
thresholding. Two tests are investigated, which are designed for better power
performance when the two population mean vectors differ only in sparsely
populated coordinates. The first test is constructed by carrying out
thresholding to remove the non-signal bearing dimensions. The second test
combines data transformation via the precision matrix with the thresholding.
The benefits of the thresholding and the data transformations are showed by a
reduced variance of the test thresholding statistics, the improved power and a
wider detection region of the tests. Simulation experiments and an empirical
study are performed to confirm the theoretical findings and to demonstrate the
practical implementations.Comment: 64 page
Tests alternative to higher criticism for high-dimensional means under sparsity and column-wise dependence
We consider two alternative tests to the Higher Criticism test of Donoho and
Jin [Ann. Statist. 32 (2004) 962-994] for high-dimensional means under the
sparsity of the nonzero means for sub-Gaussian distributed data with unknown
column-wise dependence. The two alternative test statistics are constructed by
first thresholding and statistics based on the sample means,
respectively, followed by maximizing over a range of thresholding levels to
make the tests adaptive to the unknown signal strength and sparsity. The two
alternative tests can attain the same detection boundary of the Higher
Criticism test in [Ann. Statist. 32 (2004) 962-994] which was established for
uncorrelated Gaussian data. It is demonstrated that the maximal
-thresholding test is at least as powerful as the maximal
-thresholding test, and both the maximal and -thresholding
tests are at least as powerful as the Higher Criticism test.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1168 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Linearized Tensor Renormalization Group Algorithm for Thermodynamics of Quantum Lattice Models
A linearized tensor renormalization group (LTRG) algorithm is proposed to
calculate the thermodynamic properties of one-dimensional quantum lattice
models, that is incorporated with the infinite time-evolving block decimation
technique, and allows for treating directly the two-dimensional transfer-matrix
tensor network. To illustrate its feasibility, the thermodynamic quantities of
the quantum XY spin chain are calculated accurately by the LTRG, and the
precision is shown to be comparable with (even better than) the transfer matrix
renormalization group (TMRG) method. Unlike the TMRG scheme that can only deal
with the infinite chains, the present LTRG algorithm could treat both finite
and infinite systems, and may be readily extended to boson and fermion quantum
lattice models.Comment: published versio
Helical edge and surface states in HgTe quantum wells and bulk insulators
The quantum spin Hall (QSH) effect is the property of a new state of matter
which preserves time-reversal, has an energy gap in the bulk, but has
topologically robust gapless states at the edge. Recently, it has been shown
that HgTe quantum wells realize this novel effect. In this work, we start from
realistic tight-binding models and demonstrate the existence of the helical
edge states in HgTe quantum wells and calculate their physical properties. We
also show that 3d HgTe is a topological insulator under uniaxial strain, and
show that the surface states are described by single-component massless
relativistic Dirac fermions in 2+1 dimensions. Experimental predictions are
made based on the quantitative results obtained from realistic calculations.Comment: 5 page
Quantum Anomalous Hall Effect in HgMnTe Quantum Wells
The quantum Hall effect is usually observed when the two-dimensional electron
gas is subjected to an external magnetic field, so that their quantum states
form Landau levels. In this work we predict that a new phenomenon, the quantum
anomalous Hall effect, can be realized in HgMnTe quantum wells,
without the external magnetic field and the associated Landau levels. This
effect arises purely from the spin polarization of the atoms, and the
quantized Hall conductance is predicted for a range of quantum well thickness
and the concentration of the atoms. This effect enables dissipationless
charge current in spintronics devices.Comment: 5 pages, 3 figures. For high resolution figures see final published
version when availabl
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