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

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.