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A case-deletion diagnostic for penalized calibration estimators and BLUP under linear mixed models in survey sampling

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  • Barranco-Chamorro, I.
  • Jiménez-Gamero, M.D.
  • Mayor-Gallego, J.A.
  • Moreno-Rebollo, J.L.

Abstract

The penalized calibration technique in survey sampling combines usual calibration and soft calibration by introducing a penalty term. Certain relevant estimates in survey sampling can be considered as penalized calibration estimates obtained as particular cases from an optimization problem with a common basic structure. In this framework, a case deletion diagnostic is proposed for a class of penalized calibration estimators including both design-based and model-based estimators. The diagnostic compares finite population parameter estimates and can be calculated from quantities related to the full data set. The resulting diagnostic is a function of the residual and leverage, as other diagnostics in regression models, and of the calibration weight, a singular feature in survey sampling. Moreover, a particular case, which includes the basic unit level model for small area estimation, is considered. Both a real and an artificial example are included to illustrate the diagnostic proposed. The results obtained clearly show that the proposed diagnostic depends on the calibration and soft-calibration variables, on the penalization term, as well as on the parameter to estimate.

Suggested Citation

  • Barranco-Chamorro, I. & Jiménez-Gamero, M.D. & Mayor-Gallego, J.A. & Moreno-Rebollo, J.L., 2015. "A case-deletion diagnostic for penalized calibration estimators and BLUP under linear mixed models in survey sampling," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 18-33.
    • Handle: RePEc:eee:csdana:v:87:y:2015:i:c:p:18-33
    DOI: 10.1016/j.csda.2015.01.004
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    References listed on IDEAS

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    1. Bo‐Cheng Wei & Yue‐Qing Hu & Wing‐Kam Fung, 1998. "Generalized Leverage and its Applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 25-37, March.
    2. J.-F. Beaumont & D. Haziza & A. Ruiz-Gazen, 2013. "A unified approach to robust estimation in finite population sampling," Biometrika, Biometrika Trust, vol. 100(3), pages 555-569.
    3. Temesgen Zewotir & Jacky Galpin, 2007. "A unified approach on residuals, leverages and outliers in the linear mixed model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 58-75, May.
    4. M. Jiménez-Gamero & Juan Moreno-Rebollo & Juan Muñoz-Pichardo & Ana Muñoz-Reyes, 2005. "Influence diagnostics in regression with complex designs through conditional bias," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(2), pages 515-542, December.
    5. Ray Chambers & Nikos Tzavidis, 2006. "M-quantile models for small area estimation," Biometrika, Biometrika Trust, vol. 93(2), pages 255-268, June.
    6. Juvêncio S. Nobre & Julio M. Singer, 2011. "Leverage analysis for linear mixed models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 1063-1072, February.
    7. Barranco-Chamorro, I. & Jiménez-Gamero, M.D. & Moreno-Rebollo, J.L. & Muñoz-Pichardo, J.M., 2012. "Case-deletion type diagnostics for calibration estimators in survey sampling," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2219-2236.
    8. Zaslavsky A. M. & Schenker N. & Belin T. R., 2001. "Downweighting Influential Clusters in Surveys: Application to the 1990 Post Enumeration Survey," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 858-869, September.
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