17,496 research outputs found
High-jet relations of the heat kernel embedding map and applications
For any compact Riemannian manifold and its heat kernel embedding map
from M into constructed in [BBG], we study the higher derivatives
of with respect to an orthonormal basis at on . As the heat flow
time goes to 0, it turns out the limiting angles between these derivative
vectors are universal constants independent on , and the choice of
orthonormal basis. Geometric applications to the mean curvature and the
Riemannian curvature are given. Some algebraic structures of the infinite jet
space of are explored.Comment: 28 pages, related references on random functions are adde
Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA--GARCH/IGARCH models
This paper investigates the asymptotic theory of the quasi-maximum
exponential likelihood estimators (QMELE) for ARMA--GARCH models. Under only a
fractional moment condition, the strong consistency and the asymptotic
normality of the global self-weighted QMELE are obtained. Based on this
self-weighted QMELE, the local QMELE is showed to be asymptotically normal for
the ARMA model with GARCH (finite variance) and IGARCH errors. A formal
comparison of two estimators is given for some cases. A simulation study is
carried out to assess the performance of these estimators, and a real example
on the world crude oil price is given.Comment: Published in at http://dx.doi.org/10.1214/11-AOS895 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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