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On the block maxima method in extreme value theory: PWM estimators. (English) Zbl 1310.62064

Summary: In extreme value theory, there are two fundamental approaches, both widely used: the block maxima (BM) method and the peaks-over-threshold (POT) method. Whereas much theoretical research has gone into the POT method, the BM method has not been studied thoroughly. The present paper aims at providing conditions under which the BM method can be justified. We also provide a theoretical comparative study of the methods, which is in general consistent with the vast literature on comparing the methods all based on simulated data and fully parametric models. The results indicate that the BM method is a rather efficient method under usual practical conditions.
In this paper, we restrict attention to the i.i.d. case and focus on the probability weighted moment (PWM) estimators of [J. R. M. Hosking et al., “Estimation of the generalized extreme-value distribution by the method of probability-weighted moments”, Technometrics 27, No. 3, 251–261 (1985), http://www.jstor.org/stable/1269706].

MSC:

62G32 Statistics of extreme values; tail inference
62G20 Asymptotic properties of nonparametric inference
62G30 Order statistics; empirical distribution functions
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References:

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