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Model-based variance estimation in two-dimensional systematic sampling

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Abstract

A variance estimator for the mean of a systematic sample in two dimensions is proposed and analyzed. The estimation strategy relies on a super-population model which follows a spatial auto-regressive structure and allows for the presence of covariates. The small sample properties of the proposed procedure are analyzed by simulations: the model-based estimation strategy shows an excellent performance in a variety of situations which are common in real situations.

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Notes

  1. For a more comprehensive review of the variance estimation methods and spatial sampling, see Wolter [12], Fuller [8] and Benedetti et al. [3].

  2. The maximum eigenvalue of \(\varvec{W}\) for \(K=1\) approximately equals 100.7468.

References

  1. Ambrosio Flores, L., Iglesias Martínez, L., Marín Ferrer, C.: Systematic sample design for the estimation of spatial means. Environmetrics 14(1), 45–61 (2003)

    Article  Google Scholar 

  2. Bartolucci, F., Montanari, G.E.: A new class of unbiased estimators of the variance of the systematic sample mean. Journal of Statistical Planning and Inference 136(4), 1512–1525 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Benedetti, R., Piersimoni, F., Postiglione, P.: Sampling Spatial Units for Agricultural Surveys. Springer (2015)

  4. Benedetti, R., Espa, G., Taufer, E.: Model-based variance estimation in non-measurable spatial designs. Journal of Statistical Planning and Inference 181, 52–61 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cliff, A.D., Ord, K.: Spatial Processes: Models and Applications. Pion (1981)

  6. Das, A.: Two dimensional systematic sampling and the associated stratified and random sampling. Sankhyā: The Indian Journal of Statistics pp 95–108 (1950)

  7. D’Orazio, M.: Estimating the variance of the sample mean in two-dimensional systematic sampling. Journal of Agricultural, Biological, and Environmental Statistics 8(3), 280–295 (2003)

    Article  Google Scholar 

  8. Fuller, W.A.: Sampling statistics, vol 560. John Wiley & Sons (2011)

  9. LeSage, J.P., Pace, R.K.: Introduction to Spatial Econometrics. Chapmann&Hall (2009)

  10. Montanari, G.E., Bartolucci, F.: On estimating the variance of the systematic sample mean. Statistical Methods & Applications 7(2), 185–196 (1998)

    Google Scholar 

  11. Opsomer, J.D., Francisco-Fernández, M., Li, X.: Model-based non-parametric variance estimation for systematic sampling. Scandinavian Journal of Statistics 39(3), 528–542 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wolter, K.: Introduction to variance estimation. Springer Science & Business Media (2007)

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Authors and Affiliations

  1. Universita degli Studi di Trento, Trento, Italy

    Giuseppe Espa, Diego Giuliani, Flavio Santi & Emanuele Taufer

Authors
  1. Giuseppe Espa
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  2. Diego Giuliani
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  3. Flavio Santi
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  4. Emanuele Taufer
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Corresponding author

Correspondence to Diego Giuliani.

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Espa, G., Giuliani, D., Santi, F. et al. Model-based variance estimation in two-dimensional systematic sampling. METRON 75, 265–275 (2017). https://doi.org/10.1007/s40300-017-0125-z

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  • DOI: https://doi.org/10.1007/s40300-017-0125-z

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