Estimating Heavy-Tail Exponents Through Max Self-Similarity

: In this paper, a novel approach to the problem of estimating the heavy–tail exponent α > 0 of a distribution is proposed. It is based on the fact that block–maxima of size m of the independent and identically distributed data scale at a rate of m1/α . This scaling rate can be captured well by the max–spectrum plot of the data that leads to regression based estimators. Consistency and asymptotic normality of these estimators is established under mild conditions on the behavior of the tail of the distribution. The results are obtained by establishing bounds on the rate of convergence of moment–type functionals of heavy–tailed maxima. Such bounds often yield exact rates of convergence and are of independent interest. Practical issues on the automatic selection of tuning parameters for the estimators and corresponding confidence intervals are also addressed. Extensive numerical simulations show that the proposed method proves competitive for both small and large sample si...

• Type: Journal
• Year: 2011
• Where: TIT
• Authors: Stilian Stoev, George Michailidis, Murad S. Taqqu
• Keywords: AMS 2000 Subject, Estimators, Hill Plot, TIT 2011