Tail Estimation Based on Numbers of Near m-Extremes

Samuel Müller ()
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Samuel Müller: University of Bern

Methodology and Computing in Applied Probability, 2003, vol. 5, issue 2, 197-210

Abstract: Abstract Let $$\left\{ {{\text{X}}_n ,n \geqslant 1} \right\}$$ be a sequence of independent random variables with common continuous distribution function F having finite upper endpoint. A new tail index estimator γ^ n is defined based on only two numbers of near m-extremes $$K_n \left( {a_i ,m} \right) = {\text{\# }}\left\{ {{\text{j:X}}_{\left( {n - m + :1} \right)} - a_i a 1 > 0. The weak and almost sure convergence of γ^ n to the tail index γ, as well as the asymptotic distribution is given. Moreover, the asymptotic distribution of K n (a n , m) for a n → 0 is derived.

Keywords: Distribution Function; Order Statistic; Asymptotic Distribution; Independent Random Variable; Continuous Distribution (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/A:1024509818767

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