Bispectrum estimation for a continuous-time stationary process from random sampling
Résumé
We propose an asymptotically unbiased and consistent estimate of the bispectrum of a stationary continuous-time process X = {X(t)}t∈ℝ. The estimate is constructed from observations obtained by a random sampling of the time by {X(τk)}k∈ℤ, where {τk}k∈ℤ is a sequence of real random variables, generated from a Poisson counting process. Moreover, we establish the asymptotic normality of the constructed estimate.