1,256 research outputs found
Confidence Bands for Distribution Functions: A New Look at the Law of the Iterated Logarithm
We present a general law of the iterated logarithm for stochastic processes
on the open unit interval having subexponential tails in a locally uniform
fashion. It applies to standard Brownian bridge but also to suitably
standardized empirical distribution functions. This leads to new
goodness-of-fit tests and confidence bands which refine the procedures of Berk
and Jones (1979) and Owen (1995). Roughly speaking, the high power and accuracy
of the latter procedures in the tail regions of distributions are essentially
preserved while gaining considerably in the central region
A law of the iterated logarithm for Grenander's estimator
In this note we prove the following law of the iterated logarithm for the
Grenander estimator of a monotone decreasing density: If , , and is continuous in a neighborhood of , then \begin{eqnarray*}
\limsup_{n\rightarrow \infty} \left ( \frac{n}{2\log \log n} \right )^{1/3} (
\widehat{f}_n (t_0 ) - f(t_0) ) = \left| f(t_0) f'(t_0)/2 \right|^{1/3} 2M
\end{eqnarray*} almost surely where and T_g \equiv \mbox{argmax}_u \{ g(u) - u^2 \} ; here is the two-sided Strassen limit set on . The proof relies on laws of the
iterated logarithm for local empirical processes, Groeneboom's switching
relation, and properties of Strassen's limit set analogous to distributional
properties of Brownian motion.Comment: 11 pages, 3 figure
Marshall's lemma for convex density estimation
Marshall's [Nonparametric Techniques in Statistical Inference (1970)
174--176] lemma is an analytical result which implies --consistency
of the distribution function corresponding to the Grenander [Skand.
Aktuarietidskr. 39 (1956) 125--153] estimator of a non-decreasing probability
density. The present paper derives analogous results for the setting of convex
densities on .Comment: Published at http://dx.doi.org/10.1214/074921707000000292 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
The density ratio of Poisson binomial versus Poisson distributions
Let be the probability that a sum of independent Bernoulli random
variables with parameters equals , where
is finite. We prove two inequalities for
the maximal ratio , where is the weight
function of the Poisson distribution with parameter
Combination of endobronchial bronchoscopic debulking and bronchoplastic segmentectomy of an obstructive neuroendocrine tumour: probably the least invasive approach.
We report the case of a female patient with an obstructing well-differentiated neuroendocrine tumour in the apical segment of the completely atelectatic right lower lobe. Bronchoscopic debulking of the tumour lead to re-ventilation of the remaining lobe, allowing to perform a lung-sparing bronchoplastic resection of the affected segment by uniportal video-assisted thoracic surgery
Implicit complexity for coinductive data: a characterization of corecurrence
We propose a framework for reasoning about programs that manipulate
coinductive data as well as inductive data. Our approach is based on using
equational programs, which support a seamless combination of computation and
reasoning, and using productivity (fairness) as the fundamental assertion,
rather than bi-simulation. The latter is expressible in terms of the former. As
an application to this framework, we give an implicit characterization of
corecurrence: a function is definable using corecurrence iff its productivity
is provable using coinduction for formulas in which data-predicates do not
occur negatively. This is an analog, albeit in weaker form, of a
characterization of recurrence (i.e. primitive recursion) in [Leivant, Unipolar
induction, TCS 318, 2004].Comment: In Proceedings DICE 2011, arXiv:1201.034
Assessing the cost of global biodiversity and conservation knowledge
Knowledge products comprise assessments of authoritative information supported by stan-dards, governance, quality control, data, tools, and capacity building mechanisms. Considerable resources are dedicated to developing and maintaining knowledge productsfor biodiversity conservation, and they are widely used to inform policy and advise decisionmakers and practitioners. However, the financial cost of delivering this information is largelyundocumented. We evaluated the costs and funding sources for developing and maintain-ing four global biodiversity and conservation knowledge products: The IUCN Red List ofThreatened Species, the IUCN Red List of Ecosystems, Protected Planet, and the WorldDatabase of Key Biodiversity Areas. These are secondary data sets, built on primary datacollected by extensive networks of expert contributors worldwide. We estimate that US116–204 million), plus 293 person-years of volunteer time (range: 278–308 person-years) valued at US12–16 million), were invested inthese four knowledge products between 1979 and 2013. More than half of this financingwas provided through philanthropy, and nearly three-quarters was spent on personnelcosts. The estimated annual cost of maintaining data and platforms for three of these knowl-edge products (excluding the IUCN Red List of Ecosystems for which annual costs were notpossible to estimate for 2013) is US6.2–6.7 million). We esti-mated that an additional US12 million. These costs are much lower than those tomaintain many other, similarly important, global knowledge products. Ensuring that biodi-versity and conservation knowledge products are sufficiently up to date, comprehensiveand accurate is fundamental to inform decision-making for biodiversity conservation andsustainable development. Thus, the development and implementation of plans for sustain-able long-term financing for them is critical
The Hubble Space Telescope Wide Field Camera 3 Early Release Science data: Panchromatic Faint Object Counts for 0.2-2 microns wavelength
We describe the Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) Early
Release Science (ERS) observations in the Great Observatories Origins Deep
Survey (GOODS) South field. The new WFC3 ERS data provide calibrated, drizzled
mosaics in the UV filters F225W, F275W, and F336W, as well as in the near-IR
filters F098M (Ys), F125W (J), and F160W (H) with 1-2 HST orbits per filter.
Together with the existing HST Advanced Camera for Surveys (ACS) GOODS-South
mosaics in the BViz filters, these panchromatic 10-band ERS data cover 40-50
square arcmin at 0.2-1.7 {\mu}m in wavelength at 0.07-0.15" FWHM resolution and
0.090" Multidrizzled pixels to depths of AB\simeq 26.0-27.0 mag (5-{\sigma})
for point sources, and AB\simeq 25.5-26.5 mag for compact galaxies.
In this paper, we describe: a) the scientific rationale, and the data taking
plus reduction procedures of the panchromatic 10-band ERS mosaics; b) the
procedure of generating object catalogs across the 10 different ERS filters,
and the specific star-galaxy separation techniques used; and c) the reliability
and completeness of the object catalogs from the WFC3 ERS mosaics. The
excellent 0.07-0.15" FWHM resolution of HST/WFC3 and ACS makes star- galaxy
separation straightforward over a factor of 10 in wavelength to AB\simeq 25-26
mag from the UV to the near-IR, respectively.Comment: 51 pages, 71 figures Accepted to ApJS 2011.01.2
Deep HST Observations of Star Clusters in NGC 1275
We present an analysis of compact star clusters in deep HST/WFPC2 images of
NGC 1275. B and R band photometry of roughly 3000 clusters shows a bimodality
in the B-R colors, suggesting that distinct old and young cluster populations
are present. The small spread in the colors of the blue clusters is consistent
with the hypothesis that they are a single age population, with an inferred age
of 0.1 to 1 Gyr. The luminosity function shows increasing numbers of blue
clusters to the limit of our photometry, which reaches several magnitudes past
the turnover predicted if the cluster population were identical to current
Galactic globulars seen at a younger age. The blue clusters have a spatial
distribution which is more centrally peaked than that of the red clusters. The
individual clusters are slightly resolved, with core radii <~ 0.75 pc if they
have modified Hubble profiles. We estimate the specific frequencies of the old
and young populations and discuss the uncertainties in these estimates. We find
that the specific frequency of the young population in NGC 1275 is currently
larger than that of the old population and will remain so as the young
population evolves, even if the majority of the low mass clusters are
eventually destroyed. If the young population formed during a previous merger,
this suggests that mergers can increase the specific frequency of globulars in
a galaxy. However, the presently observed young population likely contains too
few clusters to have a significant impact on the overall specific frequency as
it will be observed in the future.Comment: 26 pages, 9 figures, to be published in the Astronomical Journa
Measurement of the cross-section and charge asymmetry of bosons produced in proton-proton collisions at TeV with the ATLAS detector
This paper presents measurements of the and cross-sections and the associated charge asymmetry as a
function of the absolute pseudorapidity of the decay muon. The data were
collected in proton--proton collisions at a centre-of-mass energy of 8 TeV with
the ATLAS experiment at the LHC and correspond to a total integrated luminosity
of 20.2~\mbox{fb^{-1}}. The precision of the cross-section measurements
varies between 0.8% to 1.5% as a function of the pseudorapidity, excluding the
1.9% uncertainty on the integrated luminosity. The charge asymmetry is measured
with an uncertainty between 0.002 and 0.003. The results are compared with
predictions based on next-to-next-to-leading-order calculations with various
parton distribution functions and have the sensitivity to discriminate between
them.Comment: 38 pages in total, author list starting page 22, 5 figures, 4 tables,
submitted to EPJC. All figures including auxiliary figures are available at
https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2017-13
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