7,005 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
Quasi-invariance of countable products of Cauchy measures under non-unitary dilations
Consider an infinite sequence (Un)n∈N of independent Cauchy random variables, defined by a sequence (δn)n∈N of location parameters and a sequence (γn)n∈N of scale parameters. Let (Wn)n∈N be another infinite sequence of independent Cauchy random variables defined by the same sequence of location parameters and the sequence (σnγn)n∈N of scale parameters, with σn≠0 for all n∈N. Using a result of Kakutani on equivalence of countably infinite product measures, we show that the laws of (Un)n∈N and (Wn)n∈N are equivalent if and only if the sequence (|σn|−1)n∈N is square-summable
Equivalence of weak and strong modes of measures on topological vector spaces
A strong mode of a probability measure on a normed space can be defined
as a point such that the mass of the ball centred at uniformly
dominates the mass of all other balls in the small-radius limit. Helin and
Burger weakened this definition by considering only pairwise comparisons with
balls whose centres differ by vectors in a dense, proper linear subspace of
, and posed the question of when these two types of modes coincide. We show
that, in a more general setting of metrisable vector spaces equipped with
measures that are finite on bounded sets, the density of and a uniformity
condition suffice for the equivalence of these two types of modes. We
accomplish this by introducing a new, intermediate type of mode. We also show
that these modes can be inequivalent if the uniformity condition fails. Our
results shed light on the relationships between among various notions of
maximum a posteriori estimator in non-parametric Bayesian inference.Comment: 22 pages, 3 figure
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
Strong convergence rates of probabilistic integrators for ordinary differential equations
Probabilistic integration of a continuous dynamical system is a way of
systematically introducing model error, at scales no larger than errors
introduced by standard numerical discretisation, in order to enable thorough
exploration of possible responses of the system to inputs. It is thus a
potentially useful approach in a number of applications such as forward
uncertainty quantification, inverse problems, and data assimilation. We extend
the convergence analysis of probabilistic integrators for deterministic
ordinary differential equations, as proposed by Conrad et al.\ (\textit{Stat.\
Comput.}, 2017), to establish mean-square convergence in the uniform norm on
discrete- or continuous-time solutions under relaxed regularity assumptions on
the driving vector fields and their induced flows. Specifically, we show that
randomised high-order integrators for globally Lipschitz flows and randomised
Euler integrators for dissipative vector fields with polynomially-bounded local
Lipschitz constants all have the same mean-square convergence rate as their
deterministic counterparts, provided that the variance of the integration noise
is not of higher order than the corresponding deterministic integrator. These
and similar results are proven for probabilistic integrators where the random
perturbations may be state-dependent, non-Gaussian, or non-centred random
variables.Comment: 25 page
Diagnostics of accelerating plasma Semiannual progress report, 1 Sep. 1968 - 28 Feb. 1969
Accelerating plasma diagnostics - validity of local thermal equilibrium assumption in electromagnetic shock tubes, and current-sheet velocity in coaxial plasma accelerato
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
Pengaruh Kepuasan Kerja terhadap Kinerja Karyawan melalui Motivasi Kerja pada CV. Union Event Planner
Sumber daya manusia dapat menjadi kunci Perusahaan untuk keberhasilan. CV Union Event Planner adalah Perusahaan yang bergerak di bidang event organizer. Fenomena kinerja karyawan yang tidak maksimal, dan kesalahan yang dilakukan karyawan menjadi salah satu masalah di Perusahaan ini. Penelitian ini bertujuan untuk mengetahui pengaruh kepuasan kerja terhadap kinerja karyawan melalui motivasi kerja. Metode yang digunakan adalah kuantitatif dengan sampel penelitian sebanyak 57 karyawan CV. Union Event Planner. Berdasarkan hasil analisis data, dapat disimpulkan bahwa kepuasan kerja berpengaruh signifikan terhadap motivasi kerja karyawan CV. Union Event Planner, motivasi kerja beserta kepuasan kerja berpengaruh signifikan terhadap kinerja karyawan
Diagnostics of accelerating plasma Semiannual progress report, 1 Mar. - 31 Aug. 1968
Plasma diagnostics in electromagnetically driven shock tubes using laser scattering methods as compared to spectroscopic technique
Exchange coupling between two ferromagnetic electrodes separated by a graphene nanoribbon
In this study, based on the self-energy method and the total energy
calculation, the indirect exchange coupling between two semi-infinite
ferromagnetic strips (FM electrodes) separated by metallic graphene nanoribbons
(GNRs) is investigated. In order to form a FM/GNR/FM junction, a graphitic
region of finite length is coupled to the FM electrodes along graphitic zigzag
or armchair interfaces of width . The numerical results show that, the
exchange coupling strength which can be obtained from the difference between
the total energies of electrons in the ferromagnetic and antiferromagnetic
couplings, has an oscillatory behavior, and depends on the Fermi energy and the
length of the central region.Comment: 4 pages, 6 figures, International Conference on Theoretical Physics
'Dubna-Nano2008
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