5,423 research outputs found
Density deconvolution from repeated measurements without symmetry assumption on the errors
We consider deconvolution from repeated observations with unknown error
distribution. So far, this model has mostly been studied under the additional
assumption that the errors are symmetric.
We construct an estimator for the non-symmetric error case and study its
theoretical properties and practical performance. It is interesting to note
that we can improve substantially upon the rates of convergence which have so
far been presented in the literature and, at the same time, dispose of most of
the extremely restrictive assumptions which have been imposed so far
Nonparametric Methods in Astronomy: Think, Regress, Observe -- Pick Any Three
Telescopes are much more expensive than astronomers, so it is essential to
minimize required sample sizes by using the most data-efficient statistical
methods possible. However, the most commonly used model-independent techniques
for finding the relationship between two variables in astronomy are flawed. In
the worst case they can lead without warning to subtly yet catastrophically
wrong results, and even in the best case they require more data than necessary.
Unfortunately, there is no single best technique for nonparametric regression.
Instead, we provide a guide for how astronomers can choose the best method for
their specific problem and provide a python library with both wrappers for the
most useful existing algorithms and implementations of two new algorithms
developed here.Comment: 19 pages, PAS
A Method for Ultrashort Electron Pulse Shape-Measurement Using Coherent Synchrotron Radiation
In this paper we discuss a method for nondestructive measurements of the
longitudinal profile of sub-picosecond electron bunches for X-Ray Free Electron
Lasers (XFELs). The method is based on the detection of the Coherent
Synchrotron Radiation (CSR) spectrum produced by a bunch passing a dipole
magnet system. This work also contains a systematic treatment of synchrotron
radiation theory which lies at the basis of CSR. Standard theory of synchrotron
radiation uses several approximations whose applicability limits are often
forgotten: here we present a systematic discussion about these assumptions.
Properties of coherent synchrotron radiation from an electron moving along an
arc of a circle are then derived and discussed. We describe also an effective
and practical diagnostic technique based on the utilization of an
electromagnetic undulator to record the energy of the coherent radiation pulse
into the central cone. This measurement must be repeated many times with
different undulator resonant frequencies in order to reconstruct the modulus of
the bunch form-factor. The retrieval of the bunch profile function from these
data is performed by means of deconvolution techniques: for the present work we
take advantage of a constrained deconvolution method. We illustrate with
numerical examples the potential of the proposed method for electron beam
diagnostics at the TESLA Test Facility (TTF) accelerator. Here we choose, for
emphasis, experiments aimed at the measure of the strongly non-Gaussian
electron bunch profile in the TTF femtosecond-mode operation. We demonstrate
that a tandem combination of a picosecond streak camera and a CSR spectrometer
can be used to extract shape information from electron bunches with a narrow
leading peak and a long tail.Comment: 60 pages, 39 figure
Average derivative estimation under measurement error
In this paper, we derive the asymptotic properties of the density-weighted average derivative estimator when a regressor is contaminated with classical measurement error and the density of this error must be estimated. Average derivatives of conditional mean functions are used extensively in economics and statistics, most notably in semiparametric index models. As well as ordinary smooth measurement error, we provide results for supersmooth error distributions. This is a particularly important class of error distribution as it includes the Gaussian density. We show that under either type of measurement error, despite using nonparametric deconvolution techniques and an estimated error characteristic function, we â n-rate of convergence for the average derivative estimator. Interestingly, if the measurement error density is symmetric, the asymptotic variance of the average derivative estimator is the same irrespective of whether the error density is estimated or not. The promising finite sample performance of the estimator is shown through a Monte Carlo simulation
The scattering of muons in low Z materials
This paper presents the measurement of the scattering of 172 MeV/c muons in
assorted materials, including liquid hydrogen, motivated by the need to
understand ionisation cooling for muon acceleration.
Data are compared with predictions from the Geant 4 simulation code and this
simulation is used to deconvolute detector effects. The scattering
distributions obtained are compared with the Moliere theory of multiple
scattering and, in the case of liquid hydrogen, with ELMS. With the exception
of ELMS, none of the models are found to provide a good description of the
data. The results suggest that ionisation cooling will work better than would
be predicted by Geant 4.7.0p01.Comment: pdfeTeX V 3.141592-1.21a-2.2, 30 pages with 22 figure
Measuring angular diameters of extended sources
When measuring diameters of partially resolved sources often a technique
called gaussian deconvolution is used. This technique yields a gaussian
diameter which subsequently has to be multiplied with a conversion factor to
obtain the true angular diameter of the source. This conversion factor is a
function of the FWHM of the beam or point spread function and also depends on
the intrinsic surface brightness distribution of the source.
In this paper conversion factors are presented for a number of simple
geometries: a circular constant surface brightness disk and a spherical
constant emissivity shell, using a range of values for the inner radius. Also
more realistic geometries are studied, based on a spherically symmetric
photo-ionization model of a planetary nebula. This enables a study of optical
depth effects, a comparison between images in various emission lines and the
use of power law density distributions. It is found that the conversion factor
depends quite critically on the intrinsic surface brightness distribution,
which is usually unknown. The uncertainty is particularly large if extended
regions of low surface brightness are present in the nebula. In such cases the
use of gaussian or second moment deconvolution is not recommended.
As an alternative, a new algorithm is presented which allows the
determination of the intrinsic FWHM of the source using only the observed
surface brightness distribution and the FWHM of the beam. Tests show that this
implicit deconvolution method works well in realistic conditions, even when the
signal-to-noise is low, provided that the beam size is less than roughly 2/3 of
the observed FWHM and the beam profile can be approximated by a gaussian.Comment: 11 pages, 7 figures, accepted for publication in MNRA
On the uniform convergence of deconvolution estimators from repeated measurements
This paper studies the uniform convergence rates of Li and Vuong's (1998, Journal of Multivariate Analysis 65, 139-165; hereafter LV) nonparametric deconvolution estimator and its regularized version by Comte and Kappus (2015, Journal of Multivariate Analysis 140, 31-46) for the classical measurement error model, where repeated noisy measurements on the error-free variable of interest are available. In contrast to LV, our assumptions allow unbounded supports for the error-free variable and measurement errors. Compared to Bonhomme and Robin (2010, Review of Economic Studies 77, 491-533) specialized to the measurement error model, our assumptions do not require existence of the moment generating functions of the square and product of repeated measurements. Furthermore, by utilizing a maximal inequality for the multivariate normalized empirical characteristic function process, we derive uniform convergence rates that are faster than the ones derived in these papers under such weaker conditions
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