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Optimal sampling and estimation strategies under the linear model

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  • Desislava Nedyalkova
  • Yves Tillé

Abstract

In some cases model-based and model-assisted inferences can lead to very different estimators. These two paradigms are not so different if we search for an optimal strategy rather than just an optimal estimator, a strategy being a pair composed of a sampling design and an estimator. We show that, under a linear model, the optimal model-assisted strategy consists of a balanced sampling design with inclusion probabilities that are proportional to the standard deviations of the errors of the model and the Horvitz--Thompson estimator. If the heteroscedasticity of the model is ‚fully explainable’ by the auxiliary variables, then this strategy is also optimal in a model-based sense. Moreover, under balanced sampling and with inclusion probabilities that are proportional to the standard deviation of the model, the best linear unbiased estimator and the Horvitz--Thompson estimator are equal. Finally, it is possible to construct a single estimator for both the design and model variance. The inference can thus be valid under the sampling design and under the model. Copyright 2008, Oxford University Press.

Suggested Citation

  • Desislava Nedyalkova & Yves Tillé, 2008. "Optimal sampling and estimation strategies under the linear model," Biometrika, Biometrika Trust, vol. 95(3), pages 521-537.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:3:p:521-537
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    File URL: http://hdl.handle.net/10.1093/biomet/asn027
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    Cited by:

    1. G. Alleva & G. Arbia & P. D. Falorsi & V. Nardelli & A. Zuliani, 2023. "Optimal two-stage spatial sampling design for estimating critical parameters of SARS-CoV-2 epidemic: Efficiency versus feasibility," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 983-999, September.
    2. R. Benedetti & M. S. Andreano & F. Piersimoni, 2019. "Sample selection when a multivariate set of size measures is available," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(1), pages 1-25, March.
    3. Lin, X. Sheldon & Yang, Shuai, 2020. "Fast and efficient nested simulation for large variable annuity portfolios: A surrogate modeling approach," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 85-103.
    4. Alleva Giorgio & Falorsi Piero Demetrio & Petrarca Francesca & Righi Paolo, 2021. "Measuring the Accuracy of Aggregates Computed from a Statistical Register," Journal of Official Statistics, Sciendo, vol. 37(2), pages 481-503, June.
    5. Hasler, Caren & Tillé, Yves, 2014. "Fast balanced sampling for highly stratified population," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 81-94.
    6. Vilma Nekrašaitė-Liegė, 2011. "Some applications of panel data models in small area estimation," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 12(2), pages 265-280, October.
    7. Ina Trolle Andersen & Ute Hahn & Eva B. Vedel Jensen, 2015. "Optimal PPS Sampling with Vanishing Auxiliary Variables – with Applications in Microscopy," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1136-1148, December.
    8. Donatien Tafin Djoko & Yves Till�, 2015. "Selection of balanced portfolios to track the main properties of a large market," Quantitative Finance, Taylor & Francis Journals, vol. 15(2), pages 359-370, February.
    9. Alfio Marazzi & Yves Tillé, 2017. "Using past experience to optimize audit sampling design," Review of Quantitative Finance and Accounting, Springer, vol. 49(2), pages 435-462, August.
    10. Yves Tillé, 2022. "Some Solutions Inspired by Survey Sampling Theory to Build Effective Clinical Trials," International Statistical Review, International Statistical Institute, vol. 90(3), pages 481-498, December.
    11. Jessica Gronsbell & Molei Liu & Lu Tian & Tianxi Cai, 2022. "Efficient evaluation of prediction rules in semi‐supervised settings under stratified sampling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1353-1391, September.

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