MEAN-OF-ORDER-p LOCATION-INVARIANT EXTREME VALUE INDEX ESTIMATION
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چکیده
• A simple generalisation of the classical Hill estimator of a positive extreme value index (EVI) has been recently introduced in the literature. Indeed, the Hill estimator can be regarded as the logarithm of the mean of order p = 0 of a certain set of statistics. Instead of such a geometric mean, we can more generally consider the mean of order p (MOP) of those statistics, with p real, and even an optimal MOP (OMOP) class of EVI-estimators. These estimators are scale invariant but not location invariant. With PORT standing for peaks over random threshold, new classes of PORT-MOP and PORT-OMOP EVI-estimators are now introduced. These classes are dependent on an extra tuning parameter q, 0 ≤ q < 1, and they are both location and scale invariant, a property also played by the EVI. The asymptotic normal behaviour of those PORT classes is derived. These EVI-estimators are further studied for finite samples, through a Monte-Carlo simulation study. An adequate choice of the tuning parameters under play is put forward, and some concluding remarks are provided. Key-Words: • bootstrap and/or heuristic threshold selection; heavy tails; location/scale invariant semi-parametric estimation; Monte-Carlo simulation; optimal levels; statistics of extremes. AMS Subject Classification: • 62G32, 65C05. 274 M.I. Gomes, L. Henriques-Rodrigues and B.G. Manjunath Mean-of-Order-p Location-Invariant Extreme Value Index Estimation 275
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تاریخ انتشار 2016