2,046 research outputs found
An overview of the goodness-of-fit test problem for copulas
We review the main "omnibus procedures" for goodness-of-fit testing for
copulas: tests based on the empirical copula process, on probability integral
transformations, on Kendall's dependence function, etc, and some corresponding
reductions of dimension techniques. The problems of finding asymptotic
distribution-free test statistics and the calculation of reliable p-values are
discussed. Some particular cases, like convenient tests for time-dependent
copulas, for Archimedean or extreme-value copulas, etc, are dealt with.
Finally, the practical performances of the proposed approaches are briefly
summarized
The nested structure of urban business clusters
Although the cluster theory literature is bountiful in economics and regional
science, there is still a lack of understanding of how the geographical scales
of analysis (neighbourhood, city, region) relate to one another and impact the
observed phenomenon, and to which extent the clusters are industrially bound or
geographically consistent. In this paper, we cluster spatial economic
activities through a multi-scalar approach following percolation theory. We
consider both the industrial similarity and the geographical proximity of
firms, through their joint probability function which is constructed as a
copula. This gives rise to an emergent nested hierarchy of geoindustrial
clusters, which enables us to analyse the relationships between the different
scales, and specific industrial sectors. Using longitudinal business microdata
from the Office for National Statistics, we look at the evolution of clusters
which spans from very local groups of businesses to the metropolitan level, in
2007 and in 2014, so that the changes stemming from the financial crisis can be
observed.Comment: 20 pages, 10 figure
Stochastic cosmic ray sources and the TeV break in the all-electron spectrum
Despite significant progress over more than 100 years, no accelerator has
been unambiguously identified as the source of the locally measured flux of
cosmic rays. High-energy electrons and positrons are of particular importance
in the search for nearby sources as radiative energy losses constrain their
propagation to distances of about 1 kpc around 1 TeV. At the highest energies,
the spectrum is therefore dominated and shaped by only a few sources whose
properties can be inferred from the fine structure of the spectrum at energies
currently accessed by experiments like AMS-02, CALET, DAMPE, Fermi-LAT,
H.E.S.S. and ISS-CREAM. We present a stochastic model of the Galactic
all-electron flux and evaluate its compatibility with the measurement recently
presented by the H.E.S.S. collaboration. To this end, we have MC generated a
large sample of the all-electron flux from an ensemble of random distributions
of sources. We confirm the non-Gaussian nature of the probability density of
fluxes at individual energies previously reported in analytical computations.
For the first time, we also consider the correlations between the fluxes at
different energies, treating the binned spectrum as a random vector and
parametrising its joint distribution with the help of a pair-copula
construction. We show that the spectral break observed in the all-electron
spectrum by H.E.S.S. and DAMPE is statistically compatible with a distribution
of astrophysical sources like supernova remnants or pulsars, but requires a
rate smaller than the canonical supernova rate. This important result provides
an astrophysical interpretation of the spectrum at TeV energies and allows
differentiating astrophysical source models from exotic explanations, like dark
matter annihilation. We also critically assess the reliability of using
catalogues of known sources to model the electron-positron flux.Comment: 30 pages, 12 figures; extended discussion; accepted for publication
in JCA
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