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Calibration in Survey Sampling as an Optimization Problem

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Optimization, Control, and Applications in the Information Age

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 130))

Abstract

Calibration is a technique of adjusting sample weights routinely used in sample surveys. In this chapter, we consider calibration as an optimization problem and show that the choice of optimization function has an effect on the calibrated weights. We propose a class of functions that have several desirable properties, which includes satisfying necessary range restrictions for the weights. In this chapter, we explore the effect these new functions have on the calibrated weights.

Dedicated to Professor Panos Pardalos on the occasion of his 60th birthday

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References

  1. Bankier, M., Houle, A.M., Luc, M.: Calibration estimation in the 1991 and 1996 Canadian censuses. In: Proceedings of the Survey Research Methods Section, pp. 66–75 (1997)

    Google Scholar 

  2. Bocci, J., Beaumont, C.: Another look at ridge calibration. Metron 66(1), 5–20 (2008)

    Google Scholar 

  3. Cochran, W.G.: Sampling Techniques. Wiley, New York (1977)

    Google Scholar 

  4. Deville, J.C., Särndal, C.E.: Calibration estimators in survey sampling. J. Am. Stat. Assoc. 87(418), 376–382 (1992)

    Google Scholar 

  5. Deville, J.C., Särndal, C.E., Sautory, O.: Generalized raking procedures in survey sampling. J. Am. Stat. Assoc. 88(423), 1013–1020 (1993)

    Google Scholar 

  6. Ghalanos, A., Theussl, S.: Rsolnp: general non-linear optimization. R package version (2010)

    Google Scholar 

  7. Horvitz, D.G., Thompson, D.J.: A generalization of sampling without replacement from a finite universe. J. Am. Stat. Assoc. 47(260), 663–685 (1952)

    Google Scholar 

  8. Huang, E., Fuller, W.: Nonnegative regression estimation for sample survey data. In: Proceedings of the Social Statistics Section, vol. 21, pp. 300–305. American Statistical Association, Alexandria (1978)

    Google Scholar 

  9. Ito, K., Kunisch, K.: Augmented lagrangian methods for nonsmooth, convex optimization in Hilbert spaces. Nonlinear Anal. Theory Methods Appl. 41(5), 591–616 (2000)

    Google Scholar 

  10. Kott, P.S.: Using calibration weighting to adjust for nonresponse and coverage errors. Surv. Methodol. 32(2), 133–142 (2006)

    Google Scholar 

  11. Lundström, S., Särndal, C.E.: Calibration as a standard method for treatment of nonresponse. J. Off. Stat. 15, 305–327 (1999)

    Google Scholar 

  12. More, J.J., Wright, S.J., Pardalos, P.M.: Optimization Software Guide, vol. 14. Society for Industrial and Applied Mathematics, Philadelphia (1993)

    Google Scholar 

  13. Pardalos, P.M.: Complexity in Numerical Optimization. World Scientific, Singapore (1993)

    Google Scholar 

  14. Rao, J., Singh, A.: A ridge shrinkage method for range restricted weight calibration in survey sampling. In: Proceedings of the Section on Survey Research Methods, pp. 57–65 (1997)

    Google Scholar 

  15. Ryan, T.P.: Modern Regression Methods. Wiley, New York (2008)

    Google Scholar 

  16. Särndal, C.: The calibration approach in survey theory and practice. Surv. Methodol. 33(2), 99–119 (2007)

    Google Scholar 

  17. Singh, S., Arnab, R.: A bridge between the GREG and the linear regression estimators. In: Joint Statistical Meeting, ASA Section on Survey Research Methods, Seattle, pp. 3689–3693 (2006)

    Google Scholar 

  18. Théberge, A.: Calibration and restricted weights. Surv. Methodol. 26(1), 99–108 (2000)

    Google Scholar 

  19. Tillé, Y., Matei, A.: Rsolnp: General non-linear optimization. R package version (2013)

    Google Scholar 

  20. Vanderhoeft, C.: Generalised calibration at statistics Belgium: SPSS Module G-CALIB-S and current practices. Inst. National de Statistique (2001)

    Google Scholar 

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Correspondence to Anatoly Zhigljavsky .

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Davies, G., Gillard, J., Zhigljavsky, A. (2015). Calibration in Survey Sampling as an Optimization Problem. In: Migdalas, A., Karakitsiou, A. (eds) Optimization, Control, and Applications in the Information Age. Springer Proceedings in Mathematics & Statistics, vol 130. Springer, Cham. https://doi.org/10.1007/978-3-319-18567-5_4

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