Asymptotic lower bounds for the risk of estimators of the value of a spectral density function

Summary Discrete parameter stationary processes with joint Gaussian distributions are considered. Loss is measured by squared error. It is shown that when estimating the value of g(x ₀) of a spectral density function g the risk has an asymptotic lower bound similar to those previously obtained by Farrell 6] for the problem of density function estimation. A similar result is obtained for estimates of an entire function when risk is measured by integrated square error.