ARTICLE
ABSTRACT
In late 90ties Szarkowski observed that under the rotation pattern typical for the Labour Force Survey the recursion for the optimal estimator of the mean on a given occasion has to use estimators and observations only from three last occasions. Since the fundamental work of Patterson (1950) it had been known that for rotation patterns with "holes" it is a difficult problem to determine the depth of such recursion formulas. Under special assumptions the problem has been settled only recently in Kowalski and Wesołowski (2010). In the present paper it is shown that these assumptions are always satisfied in the case of the Szarkowski rotation pattern 110011. Moreover, explicit formulas for the coefficients of recursion are derived.
REFERENCES
CIEPIELA, P. (2004). Estimation of the mean in rotation schemes. MSc Thesis, Warsaw Univ. Techn., Fac. Math. Inform. Sci., Warsaw (in Polish)
KOWALSKI, J. (2009). Optimal estimation in rotation patterns. J. Statist. Plann. Infer. 139(4), 2429-2436.
KOWALSKI, J. (2010). Optimal recurrence estimation of the mean in rotation schemes. PhD Thesis, Warsaw Univ. Techn., Fac. Math. Inform. Sci., Warsaw (in Polish).
KOWALSKI, J. and WESOŁOWSKI, J. (2010). Recurrence optimal estimators for rotation cascade patterns with holes - unpublished manuscript
PATTERSON, H.D. (1955). Sampling on successive occasions. J. Roy. Statist. Soc. B 12, 241-255.
POPIŃSKI, W. (2006). Development of the Polish Labour Force Survey. Statist. Trans. 7(5), 1009-1030.
SZARKOWSKI, A. and WITKOWSKI, J. (1994). The Polish Labour Force Survey. Statist. Trans. 1(4), 467-483.
