@article {1164.62350,
	title = {A new class of estimators of a {\textquoteleft}{\textquoteleft}scale{\textquoteright}{\textquoteright} second order parameter.},
	journal = {Extremes},
	volume = {9},
	number = {3-4},
	year = {2006},
	note = {<p>n/a</p>
},
	pages = {193-211},
	abstract = {<p>{Let $X_i$ be i.i.d. r.v.s with heavy-tailed CDF $F(x)$ such that $$1-F(x)=(x/C)^{-1/\gamma}((1+(\beta/\rho)(x/C)^{\rho/\gamma} +\beta{\textquoteright}(x/C)^{2\rho/\gamma}(1+o(1))),$$ where $\gamma$ is the tail index ($\gamma\&gt;0$), and $\rho\&lt;0$ and $\beta$ are the {\textquoteleft}{\textquoteleft}second order parameters{\textquoteright}{\textquoteright}. The authors construct an estimator for $\beta$ based on the {\textquoteleft}{\textquoteleft}tail moments{\textquoteright}{\textquoteright} $$M_n^{(\alpha)}=(k)^{-1}\sum_{i=1}^k [{\l}og X_{n-i+1:n}-{\l}og X_{n-k:n}]^\alpha. $$ Consistency and asymptotic normality of the estimator are demonstrated. The small sample properties of the estimator are investigated via simulations.}</p>
},
	keywords = {asymptotic normality}, heavy tails, tail moments, {tail index},
	doi = {10.1007/s10687-006-0026-7},
	author = {Caeiro, Frederico and Gomes, M.Ivette}
}
