Bounds for the difference between a linear unbiased estimate and the best linear unbiased estimate

Intuitively it is obvious that if a linear unbiased estimator is only "slightly" suboptimal, the estimate cannot differ "much" from the corresponding best linear unbiased estimate for any "reasonable" observation vector. I present a Euclidean, nonstochastic bound which quantifies this heuristic notion. I then use it to constrain the difference between two vertical motion estimators from repeated precise levelling, where a candidate estimator is both known to be suboptimal at the standard model, and thought to be more resistant than the optimal estimator against deviations from it. (C) 2000 Elsevier Science Ltd. All rights reserved.