Dynamic K-Composite  estimator for an arbitrary rotation scheme

Przemysław  Ciepiela; Małgorzata Gniado; Jacek  Wesołowski; Małgorzata  Wojtyś

doi:https://doi.org/10.59170/stattrans-2012-001

Dynamic K-Composite estimator for an arbitrary rotation scheme

Przemysław Ciepiela Bank PEKAO, Warszawa, POLAND , Małgorzata Gniado Towarzystwo Ubezpieczeń na Życie "Warta", Warszawa, POLAND , Jacek Wesołowski Główny Urząd Statystyczny and Wydział Matematyki i Nauk Informacyjnych, Politechnika Warszawska, Warszawa, POLAND , Małgorzata Wojtyś Wydział Matematyki i Nauk Informacyjnych, Politechnika Warszawska, Warszawa, POLAND Statistics in Transition new series, vol. 13, 2012, 1, pages: 7-20 Published online: 1 March 2012 https://doi.org/10.59170/stattrans-2012-001

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ABSTRACT

Classical K-composite estimator was proposed in Hansen et al. (1955). Its optimality properties were developed in Rao and Graham (1964). This estimator gives an alternative solution to quasi-optimal estimation under rotation sampling when it is allowed that units leave the sample for several occasions and then come back. Such situations happen frequently in real surveys and are not covered by the recursive optimal estimator introduced by Patterson (1955). However the K-composite estimator suffers from certain disadvantages. It is designed for a stable situation in the sense that its basic parameter is kept constant on all occasions. Additionally it is restricted only to a certain family of rotation designs. Here we propose a dynamic version of the K-composite estimator (DK-composite estimator) without any restrictions on the rotation pattern. Mathematically, the algorithm, we develop, is much simpler than the one for the classical K-composite estimator with optimal weights. Moreover, it is precise, in the sense that it does not use any approximate or asymptotic approach (opposed to the method used in Rao and Graham (1964) for computing optimal weights).

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