Concerns the least-squares estimator of the mean of a covariance stationary sequence with a constant mean and an autoregressive representation of order [p]. Relative efficiency is defined as the ratio of the variances of the best linear unbiased estimator (BLUE) of the mean and the least-squares estimator (LSE). For any positive integer [p], results include: the variance of the LSE, BLUE in terms of autoregressive coefficients, variance of the BLUE, and the range of application of Ylvisaker's theorem regarding a lower bound in relative efficiency. A detailed study of relative efficiency for the second-order scheme ([p] = 2) includes bounds on parameter values for relative efficiency up to 0.80. Graphical results for the first-order scheme ([p] = 1) imply that the relative desirability of the LSE should be determined from variance as well as relative efficiency considerations. 22 pp. Ref.
This report is part of the RAND Corporation Paper series. The paper was a product of the RAND Corporation from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.
This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.
The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.