A functional Generalized Hill process and applications

2011/11/16 by Lo, Gane Samb, Deme, El Hadji
#60F05. Secondary 60B10 #60F17 #62F12 #FOS: Computer and information sciences #Methodology (stat.ME) #Primary 62E20

paper · doi:10.48550/arxiv.1111.3988

Abstract

We are concerned in this paper with the functional asymptotic behaviour of the sequence of stochastic processes T_n(f)=∑_j=1^j=kf(j)(log X_n-j+1,n-log X_n-j,n), indexed by some classes F of functions f:ℕ \backslash 0 \longmapsto ℝ₊ and where k=k(n) satisfies 1≤ k≤ n,k/n→ 0asn→ ∞. This is a functional generalized Hill process including as many new estimators of the extremal index when F is in the extremal domain. We focus in this paper on its functional and uniform asymptotic law in the new setting of weak convergence in the space of bounded real functions. The results are next particularized for explicit examples of classes F .

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