Mathematics – Statistics Theory
Scientific paper
2006-09-06
Mathematics
Statistics Theory
Scientific paper
In this paper, a novel approach to the problem of estimating the heavy-tail exponent alpha>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 m^{1/alpha}. 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 sizes and for a large range of tail exponents. The method is shown to be more robust than the classical Hill plot and is illustrated on two data sets of insurance claims and natural gas field sizes.
Michailidis George
Stoev Stilian A.
Taqqu Murad S.
No associations
LandOfFree
Estimating heavy-tail exponents through max self-similarity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Estimating heavy-tail exponents through max self-similarity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Estimating heavy-tail exponents through max self-similarity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-418859