Smoothing Parameter Selection and Alpha-Stable P-Adic Time Signals

Abstract

The estimation of the spectral density of stable p-adic signals is already done. Such estimation is based on smoothing the periodogram by using a spectral window. The convergence rate of this estimator depends on bandwidth of spectral window (called the smoothing parameter). The aim of this work is to give a technique for selecting the optimal parameter, i.e. the parameter that achieves the estimation with the best convergence rate. For that purpose, we were inspired by the cross-validation method of finding the optimal parameter. This method minimizes the integrated square error estimate.