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Multivariate shrinkage estimation of small area means and proportions


  • N. T. Longford


The familiar (univariate) shrinkage estimator of a small area mean or proportion combines information from the small area and a national survey. We define a multivariate shrinkage estimator which combines information also across subpopulations and outcome variables. The superiority of the multivariate shrinkage over univariate shrinkage, and of the univariate shrinkage over the unbiased (sample) means, is illustrated on examples of estimating the local area rates of economic activity in the subpopulations defined by ethnicity, age and sex. The examples use the sample of anonymized records of individuals from the 1991 UK census. The method requires no distributional assumptions but relies on the appropriateness of the quadratic loss function. The implementation of the method involves minimum outlay of computing. Multivariate shrinkage is particularly effective when the area level means are highly correlated and the sample means of one or a few components have small sampling and between‐area variances. Estimations for subpopulations based on small samples can be greatly improved by incorporating information from subpopulations with larger sample sizes.

Suggested Citation

  • N. T. Longford, 1999. "Multivariate shrinkage estimation of small area means and proportions," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(2), pages 227-245.
  • Handle: RePEc:bla:jorssa:v:162:y:1999:i:2:p:227-245
    DOI: 10.1111/1467-985X.00132

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    Cited by:

    1. Nicholas T. Longford, 2015. "Policy-oriented inference and the analyst-client cooperation. An example from small-area statistics," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(1), pages 65-82, May.
    2. Longford, Nicholas T., 2010. "Small area estimation with spatial similarity," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1151-1166, April.
    3. Nicholas Longford, 2014. "Incompatibility of estimation and policy objectives. An example from small-area estimation," Economics Working Papers 1447, Department of Economics and Business, Universitat Pompeu Fabra.
    4. Renato Assunção & Carl Schmertmann & Joseph Potter & Suzana Cavenaghi, 2005. "Empirical bayes estimation of demographic schedules for small areas," Demography, Springer;Population Association of America (PAA), vol. 42(3), pages 537-558, August.
    5. Golosnoy, Vasyl & Okhrin, Yarema, 2009. "Flexible shrinkage in portfolio selection," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 317-328, February.
    6. Nicholas T. Longford, 2015. "Policy-Oriented Inference And The Analyst-Client Cooperation. An Example From Small-Area Statistics," Statistics in Transition New Series, Polish Statistical Association, vol. 16(1), pages 65-82, March.
    7. Jessica Nisén & Sebastian Klüsener & Johan Dahlberg & Lars Dommermuth & Aiva Jasilioniene & Michaela Kreyenfeld & Trude Lappegård & Peng Li & Pekka Martikainen & Karel Neels & Bernhard Riederer & Sask, 2019. "Educational differences in cohort fertility across sub-national regions in Europe," MPIDR Working Papers WP-2019-018, Max Planck Institute for Demographic Research, Rostock, Germany.
    8. Mark Tranmer & Andrew Pickles & Ed Fieldhouse & Mark Elliot & Angela Dale & Mark Brown & David Martin & David Steel & Chris Gardiner, 2005. "The case for small area microdata," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(1), pages 29-49, January.
    9. Nisén, Jessica & Klüsener, Sebastian & Dahlberg, Johan & Dommermuth, Lars & Jasilioniene, Aiva & Kreyenfeld, Michaela & Lappegård, Trude & Li, Peng & Martikainen, Pekka & Neels, Karel & Riederer, Bern, 2020. "Educational differences in cohort fertility across sub-national regions in Europe," LSE Research Online Documents on Economics 106201, London School of Economics and Political Science, LSE Library.
    10. Nicholas T. Longford, 2004. "Missing data and small area estimation in the UK Labour Force Survey," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 167(2), pages 341-373, May.

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