engleski

Asymptotic properties of the empirical structure function and applications

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).

partition function; scaling functions; heavy tails

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