Optimal estimation in rotation patterns

The aim of this paper is to examine the setting of surveys repeated over time when the elements in the sample are rotated in a predesigned way. On each occasion the best linear unbiased estimator (BLUE) of the current population mean, built on all past responses, is to be found. The most straightforward approach would be to compute the estimator as a solution of a least squares problem with linear restrictions. However, this method has certain drawbacks related to the fact that the size of the response data set increases over time. We follow a different approach based on finding linear recurrence relationships between optimal estimators obtained on successive occasions. Most of the original disadvantages are then corrected. In this context we present the solution to the BLUE estimation problem for some—sufficiently regular—classes of rotation patterns.