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September 1997 Asymptotic normality of least-squares estimators of tail indices
Sándor Csörgö, László Viharos
Bernoulli 3(3): 351-370 (September 1997).


Based on least-squares considerations, Schultze and Steinebach proposed three new estimators for the tail index of a regularly varying distribution function and proved their consistency. We show that, unlike the Hill estimator, all three least-squares estimators can be centred to have normal asymptotic distributions universally over the whole model, and for two of these estimators this in fact happens at the desirable order of the norming sequence. We analyse the conditions under which asymptotic confidence intervals become possible. In a submodel, we compare the asymptotic mean squared errors of optimal versions of these and earlier estimators. The choice of the number of extreme order statistics to be used is also discussed through the investigation of the asymptotic mean squared error for a comprehensive set of examples of a general kind.


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Sándor Csörgö. László Viharos. "Asymptotic normality of least-squares estimators of tail indices." Bernoulli 3 (3) 351 - 370, September 1997.


Published: September 1997
First available in Project Euclid: 23 April 2007

zbMATH: 1066.62526
MathSciNet: MR1468310

Keywords: asymptotic confidence intervals , asymptotic mean squared errors , least-squares estimators , tail index , universal asymptotic normality

Rights: Copyright © 1997 Bernoulli Society for Mathematical Statistics and Probability

Vol.3 • No. 3 • September 1997
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