2,124 research outputs found
Adaptive variance function estimation in heteroscedastic nonparametric regression
We consider a wavelet thresholding approach to adaptive variance function
estimation in heteroscedastic nonparametric regression. A data-driven estimator
is constructed by applying wavelet thresholding to the squared first-order
differences of the observations. We show that the variance function estimator
is nearly optimally adaptive to the smoothness of both the mean and variance
functions. The estimator is shown to achieve the optimal adaptive rate of
convergence under the pointwise squared error simultaneously over a range of
smoothness classes. The estimator is also adaptively within a logarithmic
factor of the minimax risk under the global mean integrated squared error over
a collection of spatially inhomogeneous function classes. Numerical
implementation and simulation results are also discussed.Comment: Published in at http://dx.doi.org/10.1214/07-AOS509 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
New Bounds for Restricted Isometry Constants
In this paper we show that if the restricted isometry constant of
the compressed sensing matrix satisfies then -sparse
signals are guaranteed to be recovered exactly via minimization when
no noise is present and -sparse signals can be estimated stably in the noisy
case. It is also shown that the bound cannot be substantively improved. An
explicitly example is constructed in which ,
but it is impossible to recover certain -sparse signals
Effects of Neutron-Proton Short-Range Correlation on the Equation of State of Dense Neutron-Rich Nucleonic Matter
The strongly isospin-dependent tensor force leads to short-range correlations
(SRC) between neutron-proton (deuteron-like) pairs much stronger than those
between proton-proton and neutron-neutron pairs. As a result of the short-range
correlations, the single-nucleon momentum distribution develops a high-momentum
tail above the Fermi surface. Because of the strongly isospin-dependent
short-range correlations, in neutron-rich matter a higher fraction of protons
will be depleted from its Fermi sea and populate above the Fermi surface
compared to neutrons. This isospin-dependent nucleon momentum distribution may
have effects on: (1) nucleon spectroscopic factors of rare isotopes, (2) the
equation of state especially the density dependence of nuclear symmetry energy,
(3) the coexistence of a proton-skin in momentum space and a neutron-skin in
coordinate space (i.e., protons move much faster than neutrons near the surface
of heavy nuclei). In this talk, we discuss these features and their possible
experimental manifestations. As an example, SRC effects on the nuclear symmetry
energy are discussed in detail using a modified Gogny-Hartree-Fock (GHF) energy
density functional (EDF) encapsulating the SRC-induced high momentum tail (HMT)
in the single-nucleon momentum distribution
Effect of mean on variance function estimation in nonparametric regression
Variance function estimation in nonparametric regression is considered and
the minimax rate of convergence is derived. We are particularly interested in
the effect of the unknown mean on the estimation of the variance function. Our
results indicate that, contrary to the common practice, it is not desirable to
base the estimator of the variance function on the residuals from an optimal
estimator of the mean when the mean function is not smooth. Instead it is more
desirable to use estimators of the mean with minimal bias. On the other hand,
when the mean function is very smooth, our numerical results show that the
residual-based method performs better, but not substantial better than the
first-order-difference-based estimator. In addition our asymptotic results also
correct the optimal rate claimed in Hall and Carroll [J. Roy. Statist. Soc.
Ser. B 51 (1989) 3--14].Comment: Published in at http://dx.doi.org/10.1214/009053607000000901 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Robust MMSE Precoding Strategy for Multiuser MIMO Relay Systems with Switched Relaying and Side Information
In this work, we propose a minimum mean squared error (MMSE) robust base station (BS) precoding strategy based on switched relaying (SR) processing and limited transmission of side information for interference suppression in the downlink of multiuser multiple-input multiple-output (MIMO) relay systems. The BS and the MIMO relay station (RS) are both equipped with a codebook of interleaving matrices. For a given channel state information (CSI) the selection function at the BS chooses the optimum interleaving matrix from the codebook based on two optimization criteria to design the robust precoder. Prior to the payload transmission the BS sends the index corresponding to the selected interleaving matrix to the RS, where the best interleaving matrix is selected to build the optimum relay processing matrix. The entries of the codebook are randomly generated unitary matrices. Simulation results show that the performance of the proposed techniques is significantly better than prior art in the case of imperfect CSI.
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