A New Location Invariant Moment-Type Estimator and Its Asymptotic Normality
Received:March 16, 2017  Revised:March 01, 2018
Key Word: extreme value index   moment-type estimator   regular variation   location invariant   asymptotic normality  
Fund ProjectL:Supported by the National Social Science Foundation of China (Grant No.15BJY164).
Author NameAffiliation
Weiqi LIU Research Center for Management and Decision Making, Shanxi University, Shanxi 030006, P. R. China
Faculty of Finance and Banking, Shanxi University of Finance and Economics, Shanxi 030006, P. R. China 
Shanshan LIANG School of Mathematical Sciences, Shanxi University, Shanxi 030006, P. R. China 
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      The moment estimator has been widely used in extreme value theory in order to estimate the extreme value index, however it is not location invariant. In this paper, based on the moment-type estimator, we propose a new location invariant moment-type estimator, and discuss its asymptotic normality under the second order regular variation. Finally, a simulation is presented to compare this new estimator with another location invariant moment-type estimator $\hat{\gamma}_{n}^{M}(k_{0},k)$ proposed by Ling, which indicates that the new estimator has good performances.
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