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Synthetic and composite estimation under a superpopulation model

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Abstract

Under a simple superpopulation model for an arbitrary sampling design we derive optimal linear unbiased estimators/predictors of a mean in a domain. They can be viewed as synthetic and composite estimators of small area estimation theory when no auxiliary variable is available. Moreover, we show that the only requirement for optimality of a sampling strategy is to use any sampling plan of fixed sample size together with traditional estimators (as designed for simple random sampling without replacement). Finally, for symmetric sampling plans, simplified formulas (based on the first two moments of sample sizes) for optimal synthetic and composite estimators and their MSE’s are derived. Throughout the paper we consistently use the model-design setup.

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Author information

Authors and Affiliations

  1. Uniwersytet M. Kopernika, Toruń and Główny Urza̧d Statystyczny, Warszawa, Poland

    Wojciech Niemiro

  2. Politechnika Warszawska and Główny Urza̧d Statystyczny, Warszawa, Poland

    Jacek Wesołowski

Authors
  1. Wojciech Niemiro
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  2. Jacek Wesołowski
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Corresponding author

Correspondence to Wojciech Niemiro.

Additional information

Work partially supported by Polish Ministry of Science and Higher Education Grant No. 1 H02B 029 30.

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Niemiro, W., Wesołowski, J. Synthetic and composite estimation under a superpopulation model. Stat Papers 51, 497–509 (2010). https://doi.org/10.1007/s00362-008-0136-1

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  • DOI: https://doi.org/10.1007/s00362-008-0136-1

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