Estimation of the Mean of a Wide-Sense Stationary Autoregressive Sequence

摘要

The study concerns the relative efficiency of the least-squares estimator of the mean of a covariance stationary sequence that has a constant mean and an autoregressive representation of order p. The results augment those of Chipman, et al. who studied this topic for the case p = 1. Relative efficiency is defined as the ratio of the variance of the best linear unbiased estimator (BLUE) of the mean and the variance of the least-squares estimator (LSE) of the mean. Section 2 presents the problem definition and principal results. Graphical results for the first-order scheme (p = 1) in Sec. 3 imply that the relative desirability of the LSE should be based on variance as well as relative efficiency considerations.