Bootstrap based adaptation of sample myriad to characteristics of SαS distribution data

In many practical applications, noise is non-Gaussian. Heavy-tailed symmetric alpha-stable (SalphaS) distributions have been shown to describe well many natural phenomena and interference in radio engineering, acoustics, communications, etc. For processing signals corrupted by such noise, robust estimators and the corresponding techniques are widely applied. The methods based on a sample myriad (SM) are considered quasi-optimal for removal of noise with SalphaS distributions. SM estimation implies setting a tunable parameter k, desirably in an adaptive manner. However, only quite approximate recommendations concerning the selection of k for a limited size samples exist. In this paper, we study some important properties of the SM estimator with application to SalphaS distributed data. Furthermore, we propose a novel bootstrap based approach to adaptation of the tunable parameter k. By simulations, we consider its accuracy and demonstrate the effectiveness of this approach for a wide range of SalphaS distribution characteristics. Practical recommendations on the selection of parameters for the bootstrap based approach are provided and justified.