Cover: Estimation of the Mean of a Wide-Sense Stationary Autoregressive Sequence.

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

Published 1970

by George S. Fishman

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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.

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