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Small area estimation under spatial nonstationarity

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  • Chandra, Hukum
  • Salvati, Nicola
  • Chambers, Ray
  • Tzavidis, Nikos

Abstract

A geographical weighted empirical best linear unbiased predictor (GWEBLUP) for a small area average is proposed, and an estimator of its conditional mean squared error is developed. The popular empirical best linear unbiased predictor under the linear mixed model is obtained as a special case of the GWEBLUP. Empirical results using both model-based and design-based simulations, with the latter based on two real data sets, show that the GWEBLUP predictor can lead to efficiency gains when spatial nonstationarity is present in the data. A practical gain from using the GWEBLUP is in small area estimation for out of sample areas. In this case the efficient use of geographical information can potentially improve upon conventional synthetic estimation.

Suggested Citation

  • Chandra, Hukum & Salvati, Nicola & Chambers, Ray & Tzavidis, Nikos, 2012. "Small area estimation under spatial nonstationarity," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2875-2888.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:10:p:2875-2888
    DOI: 10.1016/j.csda.2012.02.006
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    References listed on IDEAS

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    1. Ray Chambers & Nikos Tzavidis, 2006. "M-quantile models for small area estimation," Biometrika, Biometrika Trust, vol. 93(2), pages 255-268, June.
    2. Monica Pratesi & Nicola Salvati, 2008. "Small area estimation: the EBLUP estimator based on spatially correlated random area effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(1), pages 113-141, February.
    3. Ugarte, M.D. & Goicoa, T. & Militino, A.F. & Durbán, M., 2009. "Spline smoothing in small area trend estimation and forecasting," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3616-3629, August.
    4. J. D. Opsomer & G. Claeskens & M. G. Ranalli & G. Kauermann & F. J. Breidt, 2008. "Non‐parametric small area estimation using penalized spline regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 265-286, February.
    5. Noel Cressie & Gardar Johannesson, 2008. "Fixed rank kriging for very large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 209-226, February.
    6. Salvati, Nicola & Chandra, Hukum & Giovanna Ranalli, M. & Chambers, Ray, 2010. "Small area estimation using a nonparametric model-based direct estimator," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2159-2171, September.
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    Cited by:

    1. Isabel Molina & Ewa Strzalkowska‐Kominiak, 2020. "Estimation of proportions in small areas: application to the labour force using the Swiss Census Structural Survey," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 281-310, January.
    2. Tomasz .Zk{a}d{l}o & Adam Chwila, 2024. "A step towards the integration of machine learning and small area estimation," Papers 2402.07521, arXiv.org.
    3. Kawakubo, Yuki & Kobayashi, Genya, 2023. "Small area estimation of general finite-population parameters based on grouped data," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    4. Timo Schmid & Nikos Tzavidis & Ralf Münnich & Ray Chambers, 2016. "Outlier Robust Small-Area Estimation Under Spatial Correlation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 806-826, September.
    5. Baldermann, Claudia & Salvati, Nicola & Schmid, Timo, 2016. "Robust small area estimation under spatial non-stationarity," Discussion Papers 2016/5, Free University Berlin, School of Business & Economics.
    6. Schmid, Timo & Tzavidis, Nikos & Münnich, Ralf & Chambers, Ray, 2015. "Outlier robust small area estimation under spatial correlation," Discussion Papers 2015/8, Free University Berlin, School of Business & Economics.

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