<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Caeiro, Frederico</style></author><author><style face="normal" font="default" size="100%">Gomes, M.Ivette</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A new class of estimators of a ``scale'' second order parameter.</style></title><secondary-title><style face="normal" font="default" size="100%">Extremes</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">asymptotic normality}</style></keyword><keyword><style  face="normal" font="default" size="100%">heavy tails</style></keyword><keyword><style  face="normal" font="default" size="100%">tail moments</style></keyword><keyword><style  face="normal" font="default" size="100%">{tail index</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2006</style></year></dates><number><style face="normal" font="default" size="100%">3-4</style></number><volume><style face="normal" font="default" size="100%">9</style></volume><pages><style face="normal" font="default" size="100%">193-211</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;{Let $X_i$ be i.i.d. r.v.s with heavy-tailed CDF $F(x)$ such that $$1-F(x)=(x/C)^{-1/\gamma}((1+(\beta/\rho)(x/C)^{\rho/\gamma} +\beta'(x/C)^{2\rho/\gamma}(1+o(1))),$$ where $\gamma$ is the tail index ($\gamma&amp;gt;0$), and $\rho&amp;lt;0$ and $\beta$ are the ``second order parameters''. The authors construct an estimator for $\beta$ based on the ``tail moments'' $$M_n^{(\alpha)}=(k)^{-1}\sum_{i=1}^k [łog X_{n-i+1:n}-łog X_{n-k:n}]^\alpha. $$ Consistency and asymptotic normality of the estimator are demonstrated. The small sample properties of the estimator are investigated via simulations.}&lt;/p&gt;
</style></abstract><notes><style face="normal" font="default" size="100%">&lt;p&gt;n/a&lt;/p&gt;
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