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A Novel Calibration Estimator in Social Surveys

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  • Antonio Arcos
  • José M. Contreras
  • María M. Rueda

Abstract

Social surveys generally assume that a sample of units (students, individuals, employees,…) is observed by two-stage selection from a finite population, which is grouped into clusters (schools, household, companies,…). This design involves sampling from two different populations: the population of schools or primary stage units and the population of students or second-stage units. Calibration estimators for student statistics can be defined by using combined information based on school totals and student totals. Auxiliary information from the units at the two stages can be calibrated by integrated weighting, as proposed by Lemaître and Dufour or Estevao and Särndal. Two calibration estimators for the population total based on unit weights are defined. The first estimator satisfies a calibration equation at the unit level, and the second one, at the cluster level. The proposed estimator shrinks the unit estimator toward the cluster. A simulation study based on two real populations is carried out to study the empirical performance of this shrinkage estimator. The populations studied were obtained from the Programme for International Student Assessment database and from the Spanish Household Budget Survey.

Suggested Citation

  • Antonio Arcos & José M. Contreras & María M. Rueda, 2014. "A Novel Calibration Estimator in Social Surveys," Sociological Methods & Research, , vol. 43(3), pages 465-489, August.
    • Handle: RePEc:sae:somere:v:43:y:2014:i:3:p:465-489
    DOI: 10.1177/0049124113507906
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    References listed on IDEAS

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    1. Sarjinder Singh, 2001. "Generalized Calibration Approach for Estimating Variance in Survey Sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 404-417, June.
    2. J. B. Copas, 1993. "The Shrinkage of Point Scoring Methods," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(2), pages 315-331, June.
    3. Jianqiang C. Wang & J. D. Opsomer, 2011. "On asymptotic normality and variance estimation for nondifferentiable survey estimators," Biometrika, Biometrika Trust, vol. 98(1), pages 91-106.
    4. D. Pfeffermann & C. J. Skinner & D. J. Holmes & H. Goldstein & J. Rasbash, 1998. "Weighting for unequal selection probabilities in multilevel models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 23-40.
    5. Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
    6. Sarjinder Singh, 2012. "On the calibration of design weights using a displacement function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(1), pages 85-107, January.
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    Cited by:

    1. Maria del Mar Rueda, 2019. "Comments on: Deville and Särndal’s calibration: revisiting a 25 years old successful optimization problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1077-1081, December.

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