5,837 research outputs found
Uniform Inference for Kernel Density Estimators with Dyadic Data
Dyadic data is often encountered when quantities of interest are associated
with the edges of a network. As such it plays an important role in statistics,
econometrics and many other data science disciplines. We consider the problem
of uniformly estimating a dyadic Lebesgue density function, focusing on
nonparametric kernel-based estimators taking the form of dyadic empirical
processes. Our main contributions include the minimax-optimal uniform
convergence rate of the dyadic kernel density estimator, along with strong
approximation results for the associated standardized and Studentized
-processes. A consistent variance estimator enables the construction of
valid and feasible uniform confidence bands for the unknown density function.
We showcase the broad applicability of our results by developing novel
counterfactual density estimation and inference methodology for dyadic data,
which can be used for causal inference and program evaluation. A crucial
feature of dyadic distributions is that they may be "degenerate" at certain
points in the support of the data, a property making our analysis somewhat
delicate. Nonetheless our methods for uniform inference remain robust to the
potential presence of such points. For implementation purposes, we discuss
inference procedures based on positive semi-definite covariance estimators,
mean squared error optimal bandwidth selectors and robust bias correction
techniques. We illustrate the empirical finite-sample performance of our
methods both in simulations and with real-world trade data, for which we make
comparisons between observed and counterfactual trade distributions in
different years. Our technical results concerning strong approximations and
maximal inequalities are of potential independent interest.Comment: Article: 23 pages, 3 figures. Supplemental appendix: 72 pages, 3
figure
Observations of the structure and evolution of solar flares with a soft X-ray telescope
Soft X ray flare events were observed with the S-056 X-ray telescope that was part of the ATM complement of instruments aboard SKYLAB. Analyses of these data are reported. The observations are summarized and a detailed discussion of the X-ray flare structures is presented. The data indicated that soft X-ray emitted by a flare come primarily from an intense well-defined core surrounded by a region of fainter, more diffuse emission. An analysis of flare evolution indicates evidence for preliminary heating and energy release prior to the main phase of the flare. Core features are found to be remarkably stable and retain their shape throughout a flare. Most changes in the overall configuration seem to be result of the appearance, disappearance or change in brightness of individual features, rather than the restructuring or reorientation of these features. Brief comparisons with several theories are presented
Yurinskii's Coupling for Martingales
Yurinskii's coupling is a popular theoretical tool for non-asymptotic
distributional analysis in mathematical statistics and applied probability,
offering a Gaussian strong approximation with an explicit error bound under
easily verified conditions. Originally stated in -norm for sums of
independent random vectors, it has recently been extended both to the
-norm, for , and to vector-valued martingales in
-norm, under some strong conditions. We present as our main result a
Yurinskii coupling for approximate martingales in -norm, under
substantially weaker conditions than those previously imposed. Our formulation
further allows for the coupling variable to follow a more general Gaussian
mixture distribution, and we provide a novel third-order coupling method which
gives tighter approximations in certain settings. We specialize our main result
to mixingales, martingales, and independent data, and derive uniform Gaussian
mixture strong approximations for martingale empirical processes. Applications
to nonparametric partitioning-based and local polynomial regression procedures
are provided.Comment: 55 pages, 1 figur
Visual saliency and semantic incongruency influence eye movements when inspecting pictures
Models of low-level saliency predict that when we first look at a photograph our first few eye movements should be made towards visually conspicuous objects. Two experiments investigated this prediction by recording eye fixations while viewers inspected pictures of room interiors that contained objects with known saliency characteristics. Highly salient objects did attract fixations earlier than less conspicuous objects, but only in a task requiring general encoding of the whole picture. When participants were required to detect the presence of a small target, then the visual saliency of nontarget objects did not influence fixations. These results support modifications of the model that take the cognitive override of saliency into account by allowing task demands to reduce the saliency weights of task-irrelevant objects. The pictures sometimes contained incongruent objects that were taken from other rooms. These objects were used to test the hypothesis that previous reports of the early fixation of congruent objects have not been consistent because the effect depends upon the visual conspicuity of the incongruent object. There was an effect of incongruency in both experiments, with earlier fixation of objects that violated the gist of the scene, but the effect was only apparent for inconspicuous objects, which argues against the hypothesis
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Tablet PCs in schools: Case study report: A report for Becta by the Open University
The publication provides an analysis of twelve case studies involving schools in England that were using Tablet PCs. The analysis is complemented by brief individual reports describing aspects of how each of these schools was using Tablet PCs
Phase behaviour of the quantum Lennard-Jones solid
The Lennard-Jones potential is perhaps one of the most widely-used models for
the interaction of uncharged particles, such as noble gas solids. The phase
diagram of the classical LJ solid is known to exhibit transitions between hcp
and fcc phases. However, the phase behaviour of the quantum Lennard-Jones solid
remains unknown. Thermodynamic integration based on path integral molecular
dynamics and lattice dynamics calculations are used to study the phase
stability of the hcp and fcc Lennard-Jones solids. The hcp phase is shown to be
stabilized by quantum effects in PIMD while fcc is shown to be favoured by
lattice dynamics, which suggests a possible re-entrant low pressure hcp phase
for highly quantum systems. Implications for the phase stability of noble gas
solids are discussed. For parameters equating to Helium, the expansion due to
zero-point vibrations is associated with quantum melting: neither crystal
structure is stable at zero pressure
Apparatus for Leak Testing Pressurized Hoses
A hose-attaching apparatus for leak-testing a pressurized hose may include a hose-attaching member. A bore may extend through the hose-attaching member. An internal annular cavity may extend coaxially around the bore. At least one of a detector probe hole and a detector probe may be connected to the internal annular cavity. At least a portion of the bore may have a diameter which is at least one of substantially equal to and less than a diameter of a hose to be leak-tested
Transforming the Productivity of People in the Built Environment: Emergence of a Digital Competency Management Ecosystem
This chapter explores how we create and support a digitally enabled, agile, competent, and ultimately, productive workforce and determines the key research questions that need to be addressed if Digital Built Britain (DBB) is to provide return on investment and succeed as the catalyst for evolving the manner in which we conceive, plan, design, construct, operate, and interact with the built environment. The proposed vision is a digital competency management ecosystem where interdependent stakeholders are incentivised to work together in coopetition to create, capture, infer, interpret, specify, integrate, accredit, apply, use, monitor, and evolve competence as a working (data) asset. This needs to be in a consistent, objective, explicit, and scalable manner, with end2end transparency and traceability for all stakeholders that overcome the challenges of competency management. Moreover, a core element must be an ecosystem organised around digital infrastructure of competency frameworks and other knowledge sources of competence, so that competency frameworks are in digital operation and dynamic context
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