12,967 research outputs found

### Asymptotics for sliced average variance estimation

In this paper, we systematically study the consistency of sliced average
variance estimation (SAVE). The findings reveal that when the response is
continuous, the asymptotic behavior of SAVE is rather different from that of
sliced inverse regression (SIR). SIR can achieve $\sqrt{n}$ consistency even
when each slice contains only two data points. However, SAVE cannot be
$\sqrt{n}$ consistent and it even turns out to be not consistent when each
slice contains a fixed number of data points that do not depend on n, where n
is the sample size. These results theoretically confirm the notion that SAVE is
more sensitive to the number of slices than SIR. Taking this into account, a
bias correction is recommended in order to allow SAVE to be $\sqrt{n}$
consistent. In contrast, when the response is discrete and takes finite values,
$\sqrt{n}$ consistency can be achieved. Therefore, an approximation through
discretization, which is commonly used in practice, is studied. A simulation
study is carried out for the purposes of illustration.Comment: Published at http://dx.doi.org/10.1214/009053606000001091 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org

### Single soft gluon emission at two loops

We study the single soft-gluon current at two loops with two energetic
partons in massless perturbative QCD, which describes, for example, the soft
limit of the two-loop amplitude for $gg\to Hg$. The results are presented as
Laurent expansions in $\epsilon$ in $D=4-2\epsilon$ spacetime dimension. We
calculate the expansion to order $\epsilon^2$ analytically, which is a
necessary ingredient for Higgs production at hadron colliders at
next-to-next-to-next-to-leading order in the soft-virtual approximation. We
also give two-loop results of the single soft-gluon current in ${\cal N}=4$
Super-Yang-Mills theory, and find that it has uniform transcendentality. By
iteration relation of splitting amplitudes, our calculations can determine the
three-loop single soft-gluon current to order $\epsilon^0$ in ${\cal N}=4$
Super-Yang-Mills theory in the limit of large $N_c$.Comment: typos corrected; journal versio

### Nonparametric checks for single-index models

In this paper we study goodness-of-fit testing of single-index models. The
large sample behavior of certain score-type test statistics is investigated. As
a by-product, we obtain asymptotically distribution-free maximin tests for a
large class of local alternatives. Furthermore, characteristic function based
goodness-of-fit tests are proposed which are omnibus and able to detect peak
alternatives. Simulation results indicate that the approximation through the
limit distribution is acceptable already for moderate sample sizes.
Applications to two real data sets are illustrated.Comment: Published at http://dx.doi.org/10.1214/009053605000000020 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org

### Efficient estimation of moments in linear mixed models

In the linear random effects model, when distributional assumptions such as
normality of the error variables cannot be justified, moments may serve as
alternatives to describe relevant distributions in neighborhoods of their
means. Generally, estimators may be obtained as solutions of estimating
equations. It turns out that there may be several equations, each of them
leading to consistent estimators, in which case finding the efficient estimator
becomes a crucial problem. In this paper, we systematically study estimation of
moments of the errors and random effects in linear mixed models.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ330 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

### Top-Quark Decay at Next-to-Next-to-Leading Order in QCD

We present the complete calculation of the top-quark decay width at
next-to-next-to-leading order in QCD, including next-to-leading electroweak
corrections as well as finite bottom quark mass and $W$ boson width effects. In
particular, we also show the first results of the fully differential decay
rates for top-quark semileptonic decay $t\to W^+(l^+\nu)b$ at
next-to-next-to-leading order in QCD. Our method is based on the understanding
of the invariant mass distribution of the final-state jet in the singular limit
from effective field theory. Our result can be used to study arbitrary
infrared-safe observables of top-quark decay with the highest perturbative
accuracy.Comment: 5 pages, 6 figures; version accepted for publication in Physical
Review Letter

### Resummation prediction on top quark transverse momentum distribution at large pT

We study the factorization and resummation of t-channel top quark transverse
momentum distribution at large pT in the SM at both the Tevatron and the LHC
with soft-collinear effective theory. The cross section in the threshold region
can be factorized into a convolution of hard, jet and soft functions. In
particular, we first calculate the NLO soft functions for this process, and
give a RG improved cross section by evolving the different functions to a
common scale. Our results show that the resummation effects increase the NLO
results by about 9%-13% and 4%-9% when the top quark pT is larger than 50 and
70 GeV at the Tevatron and the 8 TeV LHC, respectively. Also, we discuss the
scale independence of the cross section analytically, and show how to choose
the proper scales at which the perturbative expansion can converge fast.Comment: 32 pages, 10 figures, version published in Phys.Rev.

### Indirect unitarity violation entangled with matter effects in reactor antineutrino oscillations

If finite but tiny masses of the three active neutrinos are generated via the
canonical seesaw mechanism with three heavy sterile neutrinos, the 3\times 3
Pontecorvo-Maki-Nakagawa-Sakata neutrino mixing matrix V will not be exactly
unitary. This kind of indirect unitarity violation can be probed in a precision
reactor antineutrino oscillation experiment, but it may be entangled with
terrestrial matter effects as both of them are very small. We calculate the
probability of \overline{\nu}_e \to \overline{\nu}_e oscillations in a good
analytical approximation, and find that, besides the zero-distance effect, the
effect of unitarity violation is always smaller than matter effects, and their
entanglement does not appear until the next-to-leading-order oscillating terms
are taken into account. Given a 20-kiloton JUNO-like liquid scintillator
detector, we reaffirm that terrestrial matter effects should not be neglected
but indirect unitarity violation makes no difference, and demonstrate that the
experimental sensitivities to the neutrino mass ordering and a precision
measurement of \theta_{12} and \Delta_{21} \equiv m^2_2 - m^2_1 are robust.Comment: 21 pages, 6 figures, version to be published in PLB, more discussions
adde

- â€¦