Volume 14, Number 2/3

Spectral Estimate for Stable Signals with P-Adic Time and Optimal Selection of Smoothing Parameter

  Authors

Rachid SABRE¹ and Walid HORRIGUE², ¹University of Burgundy/ Institut Agro, France, ²Univ. Bourgogne
FrancheComté, France

  Abstract

The spectral density of stable signals with p-adic times is already estimated under various conditions. The estimate is made by constructing a periodogram that is subsequently smoothed by a spectral window. It is clear that the convergence rate of this estimator depends on the bandwidth of the spectral window (called the smoothing parameter). This work gives a method to select the smoothing parameter in an optimal way, i.e. the estimator converges to the spectral density with the bestrate. The method is inspired by the cross-validation method, which consists in minimizing the estimate of the integrated square error.

  Keywords

Spectral density, p-adic processes, alpha stable, random field.