Naslov
Asymptotic properties of the empirical structure function and applications

Autori
Grahovac, Danijel

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, ostalo

Skup
18th Austrian, Croatian, Hungarian, Italian and Slovenian Meeting of Young Statisticians

Mjesto i datum
Balatonfüred, Mađarska, 11.10.2013. - 13.10.2013

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
partition function; scaling functions; heavy tails

Sažetak
Empirical structure function is a variant of a sample moment statistic obtained by averaging partial sums of consecutive blocks of sampled data. Terminology comes from the theory of turbulence and multifractal stochastic processes. We analyze some asymptotic properties of this statistic in the context of stationary strong mixing sample coming from some heavy tailed distribution. In particular, we establish the rate of growth. The limit heavily depends on the value of the tail index of the underlying distribution as well as on the parameters used in the definition of structure function. This makes it possible to make inference about distribution tail. We develop a new method to detect heavy tails and identify the range of the corresponding tail index $\alpha$. A new method for the estimation of $\alpha$ is presented. We also discuss some other possible applications. The results are based on the joint work with Prof. N. Leonenko (University of Cardiff, UK), Prof. E. Taufer (University of Trento, Italy) and Mofei Jia (University of Trento, Italy).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA