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

The efficiency in estimating the mean of a weakly stationary process is investigated. Estimators are optimum provided the spectral density has a zero in t = 0 of order [lambda]. Here we study the asymptotic behavior of in case the spectral density has a zero in t = 0 of order different from [lambda]. In particular we prove that are optimum if [lambda] is greater than this order.weakly stationary processes estimation of the mean orthogonal polynomials