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Exact linear unbiased estimation in survey sampling. (With discussion). (English) Zbl 0989.62009
Summary: The concept of the linearity of estimators in finite population inference is not well defined. We propose that linearity should be defined for both estimators and estimands and that strict linearity should be related constructively to the property of unbiasedness. We establish the conditions for the class of general linear estimators, introduced by V.P. Godambe [J. R. Stat. Soc., Ser. B 17, 269-278 (1955; Zbl 0067.11406)], to be strictly linear. The ideas are extended to quadratic estimators of quadratic estimands. The implications are explored for ratio estimators, and domains of study, the latter extendible to poststratification.

62D05 Sampling theory, sample surveys
Full Text: DOI
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