1,924 research outputs found
Bootstrap and permutation tests of independence for point processes
Motivated by a neuroscience question about synchrony detection in spike train
analysis, we deal with the independence testing problem for point processes. We
introduce non-parametric test statistics, which are rescaled general
-statistics, whose corresponding critical values are constructed from
bootstrap and randomization/permutation approaches, making as few assumptions
as possible on the underlying distribution of the point processes. We derive
general consistency results for the bootstrap and for the permutation w.r.t. to
Wasserstein's metric, which induce weak convergence as well as convergence of
second order moments. The obtained bootstrap or permutation independence tests
are thus proved to be asymptotically of the prescribed size, and to be
consistent against any reasonable alternative. A simulation study is performed
to illustrate the derived theoretical results, and to compare the performance
of our new tests with existing ones in the neuroscientific literature
Adaptive estimation for Hawkes processes; application to genome analysis
The aim of this paper is to provide a new method for the detection of either
favored or avoided distances between genomic events along DNA sequences. These
events are modeled by a Hawkes process. The biological problem is actually
complex enough to need a nonasymptotic penalized model selection approach. We
provide a theoretical penalty that satisfies an oracle inequality even for
quite complex families of models. The consecutive theoretical estimator is
shown to be adaptive minimax for H\"{o}lderian functions with regularity in
: those aspects have not yet been studied for the Hawkes' process.
Moreover, we introduce an efficient strategy, named Islands, which is not
classically used in model selection, but that happens to be particularly
relevant to the biological question we want to answer. Since a multiplicative
constant in the theoretical penalty is not computable in practice, we provide
extensive simulations to find a data-driven calibration of this constant. The
results obtained on real genomic data are coherent with biological knowledge
and eventually refine them.Comment: Published in at http://dx.doi.org/10.1214/10-AOS806 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Mass fluxes for hot stars
In an attempt to understand the extraordinarily small mass-loss rates of
late-type O dwarfs, mass fluxes in the relevant part of (T_{eff}, g)-space are
derived from first principles using a previously-described code for
constructing moving reversing layers. From these mass fluxes, a weak-wind
domain is identified within which a star's rate of mass loss by a
radiatively-driven wind is less than that due to nuclear burning. The five
weak-wind stars recently analysed by Marcolino et al. (2009) fall within or at
the edge of this domain. But although the theoretical mass fluxes for these
stars are ~ 1.4 dex lower than those derived with the formula of Vink et al.
(2000), the observed rates are still not matched, a failure that may reflect
our poor understanding of low-density supersonic outflows.
Mass fluxes are also computed for two strong-wind O4 stars analysed by Bouret
et al. (2005). The predictions agree with the sharply reduced mass loss rates
found when Bouret et al. take wind clumping into account.Comment: Accepted by A&A; 6 pages, 5 figures; minor changes from v
Continuous testing for Poisson process intensities: A new perspective on scanning statistics
We propose a novel continuous testing framework to test the intensities of
Poisson Processes. This framework allows a rigorous definition of the complete
testing procedure, from an infinite number of hypothesis to joint error rates.
Our work extends traditional procedures based on scanning windows, by
controlling the family-wise error rate and the false discovery rate in a
non-asymptotic manner and in a continuous way. The decision rule is based on a
\pvalue process that can be estimated by a Monte-Carlo procedure. We also
propose new test statistics based on kernels. Our method is applied in
Neurosciences and Genomics through the standard test of homogeneity, and the
two-sample test
Concentration for norms of infinitely divisible vectors with independent components
We obtain dimension-free concentration inequalities for -norms,
, of infinitely divisible random vectors with independent coordinates
and finite exponential moments. Besides such norms, the methods and results
extend to some other classes of Lipschitz functions.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ131 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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