R. Lasser et M. Niessner, ON THE ORDER OF CONVERGENCE IN LINEAR MEAN ESTIMATION OF WEAKLY STATIONARY STOCHASTIC-PROCESSES, Stochastic processes and their applications, 47(1), 1993, pp. 143-152
The efficiency in estimating the mean of a weakly stationary process i
s investigated. Estimators M(n)lambda are optimum provided the spectra
l density has a zero in t = 0 of order lambda. Here we study the asymp
totic behavior of M(n)lambda in case the spectral density has a zero i
n t = 0 of order different from lambda. In particular we prove that M(
n)lambda are optimum if lambda is greater than this order.