87,857 research outputs found
Two sample tests for high-dimensional covariance matrices
We propose two tests for the equality of covariance matrices between two
high-dimensional populations. One test is on the whole variance--covariance
matrices, and the other is on off-diagonal sub-matrices, which define the
covariance between two nonoverlapping segments of the high-dimensional random
vectors. The tests are applicable (i) when the data dimension is much larger
than the sample sizes, namely the "large , small " situations and (ii)
without assuming parametric distributions for the two populations. These two
aspects surpass the capability of the conventional likelihood ratio test. The
proposed tests can be used to test on covariances associated with gene ontology
terms.Comment: Published in at http://dx.doi.org/10.1214/12-AOS993 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Strong stability of Nash equilibria in load balancing games
We study strong stability of Nash equilibria in the load balancing games of m (m >= 2) identical servers, in which every job chooses one of the m servers and each job wishes to minimize its cost, given by the
workload of the server it chooses.
A Nash equilibrium (NE) is a strategy profile that is resilient to unilateral deviations. Finding an NE in such a game is simple. However, an NE assignment is not stable against coordinated deviations of several jobs, while a strong Nash equilibrium (SNE) is. We study how well an
NE approximates an SNE.
Given any job assignment in a load balancing game, the improvement ratio (IR) of a deviation of a job is defined as the ratio between the pre-and post-deviation costs. An NE is said to be a ρ-approximate SNE (ρ >= 1) if there is no coalition of jobs such that each job of the coalition
will have an IR more than ρ from coordinated deviations of the coalition.
While it is already known that NEs are the same as SNEs in the 2-server load balancing game, we prove that, in the m-server load balancing game for any given m >= 3, any NE is a (5=4)-approximate SNE, which together with the lower bound already established in the literature implies that the approximation bound is tight. This closes the final gap in the literature on the study of approximation of general NEs to SNEs in the load balancing games. To establish our upper bound, we apply with novelty a powerful graph-theoretic tool
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
Critical exponents of finite temperature chiral phase transition in soft-wall AdS/QCD models
Criticality of chiral phase transition at finite temperature is investigated
in a soft-wall AdS/QCD model with symmetry,
especially for and . It is shown that in quark mass
plane() chiral phase transition is second order at a certain
critical line, by which the whole plane is divided into first order and
crossover regions. The critical exponents and , describing
critical behavior of chiral condensate along temperature axis and light quark
mass axis, are extracted both numerically and analytically. The model gives the
critical exponents of the values and
for and respectively. For
, in small strange quark mass() region, the phase transitions for
strange quark and quarks are strongly coupled, and the critical exponents
are ; when is larger than
, the dynamics of light flavors() and strange
quarks decoupled and the critical exponents for and
becomes , exactly the same as result and
the mean field result of 3D Ising model; between the two segments, there is a
tri-critical point at , at which
. In some sense, the current results is still at mean
field level, and we also showed the possibility to go beyond mean field
approximation by including the higher power of scalar potential and the
temperature dependence of dilaton field, which might be reasonable in a full
back-reaction model. The current study might also provide reasonable
constraints on constructing a realistic holographic QCD model, which could
describe both chiral dynamics and glue-dynamics correctly.Comment: 32 pages, 11 figures, regular articl
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