On the order of convergence in linear mean estimation of weakly stationary stochastic processes

AbstractThe efficiency in estimating the mean of a weakly stationary process is investigated. Estimators Mnλ are optimum provided the spectral density has a zero in t = 0 of order λ. Here we study the asymptotic behavior of Mnλ in case the spectral density has a zero in t = 0 of order different from λ. In particular we prove that Mnλ are optimum if λ is greater than this order