5,237 research outputs found
Weak convergence of the weighted empirical beta copula process
The empirical copula has proved to be useful in the construction and
understanding of many statistical procedures related to dependence within
random vectors. The empirical beta copula is a smoothed version of the
empirical copula that enjoys better finite-sample properties. At the core lie
fundamental results on the weak convergence of the empirical copula and
empirical beta copula processes. Their scope of application can be increased by
considering weighted versions of these processes. In this paper we show weak
convergence for the weighted empirical beta copula process. The weak
convergence result for the weighted empirical beta copula process is stronger
than the one for the empirical copula and its use is more straightforward. The
simplicity of its application is illustrated for weighted Cram\'er--von Mises
tests for independence and for the estimation of the Pickands dependence
function of an extreme-value copula.Comment: 19 pages, 2 figure
Weak convergence of the empirical copula process with respect to weighted metrics
The empirical copula process plays a central role in the asymptotic analysis
of many statistical procedures which are based on copulas or ranks. Among other
applications, results regarding its weak convergence can be used to develop
asymptotic theory for estimators of dependence measures or copula densities,
they allow to derive tests for stochastic independence or specific copula
structures, or they may serve as a fundamental tool for the analysis of
multivariate rank statistics. In the present paper, we establish weak
convergence of the empirical copula process (for observations that are allowed
to be serially dependent) with respect to weighted supremum distances. The
usefulness of our results is illustrated by applications to general bivariate
rank statistics and to estimation procedures for the Pickands dependence
function arising in multivariate extreme-value theory.Comment: 39 pages + 7 pages of supplementary material, 1 figur
On the Hilbert eigenvariety at exotic and CM classical weight 1 points
Let be a totally real number field and let be a classical cuspidal
-regular Hilbert modular eigenform over of parallel weight . Let
be the point on the -adic Hilbert eigenvariety corresponding to
an ordinary -stabilization of . We show that if the -adic Schanuel
Conjecture is true, then is smooth at if has CM. If we
additionally assume that is Galois, we show that the weight map
is \'etale at if has either CM or exotic projective image (which is the
case for almost all cuspidal Hilbert modular eigenforms of parallel weight
). We prove these results by showing that the completed local ring of the
eigenvariety at is isomorphic to a universal nearly ordinary Galois
deformation ring.Comment: The material in the introduction and the final sections was
reorganized. The sections on background material were substantially shortene
Biofuels in the world markets: A Computable General Equilibrium assessment of environmental costs related to land use changes
Biofuels in the world markets: A Computable General Equilibrium assessment of environmental costs related to land use changes
OECD Domestic Support and Developing Countries
domestic support, OECD, developing countries, agricultural trade, WTO
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