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Asymptotic normality of extreme value estimators on
Consider i.i.d. random elements on . We show that, under an
appropriate strengthening of the domain of attraction condition, natural
estimators of the extreme-value index, which is now a continuous function, and
the normalizing functions have a Gaussian process as limiting distribution. A
key tool is the weak convergence of a weighted tail empirical process, which
makes it possible to obtain the results uniformly on . Detailed examples
are also presented.Comment: Published at http://dx.doi.org/10.1214/009053605000000831 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Axial Anomaly and the Nucleon Spin
In this letter, we have taken a particular Lagrangian, which was introduced
to resolve U(1) problem, as an effective QCD Lagrangian, and have derived a
formula of the quark content of the nucleon spin. The difference between quark
content of the proton (\Delta\Sigma_p) and that of the neutron (\Delta\Sigma_n)
is evaluated by this formula. Neglecting the higher-order isospin corrections,
this formula can reduce to Efremov's results in the large N_c limit.Comment: (1) A few changes and corrections made following Referee. (2) The
difference between quark content of the proton (\Delta\Sigma_p) and that of
the neutron (\Delta\Sigma_n) is evaluated. Neglecting the higher-order
isospin corrections, this formula can reduce to Efremov's results in the
large N_c limi
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