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Empirical Likelihood Approach for Aligning Information from Multiple Surveys

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  • Yves G. Berger
  • Ewa Kabzińska

Abstract

When two surveys carried out separately in the same population have common variables, it might be desirable to adjust each survey's weights so that they give equal estimates for the common variables. This problem has been studied extensively and has often been referred to as alignment or numerical consistency. We develop a design‐based empirical likelihood approach for alignment and estimation of complex parameters defined by estimating equations. We focus on a general case when a single set of adjusted weights, which can be applied to both common and non‐common variables, is produced for each survey. The main contribution of the paper is to show that the impirical log‐likelihood ratio statistic is pivotal in the presence of alignment constraints. This pivotal statistic can be used to test hypotheses and derive confidence regions. Hence, the empirical likelihood approach proposed for alignment possesses the self‐normalisation property, under a design‐based approach. The proposed approach accommodates large sampling fractions, stratification and population level auxiliary information. It is particularly well suited for inference about small domains, when data are skewed. It includes implicit adjustments when the samples considerably differ in size. The confidence regions are constructed without the need for variance estimates, joint‐inclusion probabilities, linearisation and re‐sampling.

Suggested Citation

  • Yves G. Berger & Ewa Kabzińska, 2020. "Empirical Likelihood Approach for Aligning Information from Multiple Surveys," International Statistical Review, International Statistical Institute, vol. 88(1), pages 54-74, April.
  • Handle: RePEc:bla:istatr:v:88:y:2020:i:1:p:54-74
    DOI: 10.1111/insr.12337
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    References listed on IDEAS

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    1. Takis Merkouris, 2004. "Combining Independent Regression Estimators From Multiple Surveys," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1131-1139, December.
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    3. Jae Kwang Kim & J. N. K. Rao, 2012. "Combining data from two independent surveys: a model-assisted approach," Biometrika, Biometrika Trust, vol. 99(1), pages 85-100.
    4. Song Chen & Ingrid Van Keilegom, 2009. "A review on empirical likelihood methods for regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 415-447, November.
    5. Sanjay Chaudhuri & Mark S. Handcock & Michael S. Rendall, 2008. "Generalized linear models incorporating population level information: an empirical‐likelihood‐based approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 311-328, April.
    6. Berger, Yves G. & Muñoz, Juan F. & Rancourt, Eric, 2009. "Variance estimation of survey estimates calibrated on estimated control totals--An application to the extended regression estimator and the regression composite estimator," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2596-2604, May.
    7. Takis Merkouris, 2010. "Combining information from multiple surveys by using regression for efficient small domain estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 27-48, January.
    8. Wayne A. Fuller, 2009. "Some design properties of a rejective sampling procedure," Biometrika, Biometrika Trust, vol. 96(4), pages 933-944.
    9. Song Chen & Ingrid Van Keilegom, 2009. "Rejoinder on: A review on empirical likelihood methods for regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 468-474, November.
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    Cited by:

    1. Maria Mar Rueda & Maria Giovanna Ranalli & Antonio Arcos & David Molina, 2021. "Population empirical likelihood estimation in dual frame surveys," Statistical Papers, Springer, vol. 62(5), pages 2473-2490, October.

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