Asymptotic normality of location invariant heavy tail index estimator
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Motivated by Fraga Alves (Extremes 4:199–217, 2001)’s work, a new class of location invariant Hill-type estimators for the tail index of a heavy tailed distribution is proposed in the paper. Its asymptotic behavior is derived, and the optimal choice of the sample fraction is discussed by mean squared error. Asymptotic comparisons and simulation studies are presented to show that the new estimator performs well compared to the known ones.
KeywordsAsymptotic normality Location invariant index estimator Second order regular variation Tail index
AMS 2000 Subject ClassificationsPrimary—62G32 Secondary—65C05
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- Ling, C., Peng, Z., Nadarajah, S.: A location invariant moment-type estimator (II). Theory Probab. Math. Stat. 77, 167–178 (2007b)Google Scholar