Statistical Analysis of Autoregressive Spectral Estimates for Noise Corrupted Autoregressive Series.

摘要

Estimation of the spectral density function for a gaussian distributed autoregressive series from observations of a noise corrupted version is considered when the order of the autoregressive series is assumed to be known. When the high-order Yule-Walker equation estimates of the autoregressive parameters are used to form the spectral density estimate, it is shown that the estimate is weakly consistent and asymptotically normal with zero mean and finite variance. A closed form expression for the asymptotic variance is developed and the expression is analyzed for the first-order AR series case. (Author)