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Small area estimates for cross‐classifications

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  • Li‐Chun Zhang
  • Raymond L. Chambers

Abstract

Summary. We develop a class of log‐linear structural models that is suited to estimation of small area cross‐classified counts based on survey data. This allows us to account for various associ‐ ation structures within the data and includes as a special case the restricted log‐linear model underlying structure preserving estimation. The effect of survey design can be incorporated into estimation through the specification of an unbiased direct estimator and its associated covariance structure. We illustrate our approach by applying it to estimation of small area labour force characteristics in Norway.

Suggested Citation

  • Li‐Chun Zhang & Raymond L. Chambers, 2004. "Small area estimates for cross‐classifications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 479-496, May.
    • Handle: RePEc:bla:jorssb:v:66:y:2004:i:2:p:479-496
    DOI: 10.1111/j.1369-7412.2004.05266.x
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    Cited by:

    1. Alison Whitworth & Kirsten Piller & Angela Luna & Li-Chun Zhang, 2015. "Small area estimates of the population distribution by ethnic group in England: a proposal using structure preserving estimators," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(4), pages 585-602, December.
    2. Angela Luna & Li-Chun Zhang & Alison Whitworth & Kirsten Piller, 2015. "Small Area Estimates Of The Population Distribution By Ethnic Group In England: A Proposal Using Structure Preserving Estimators," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 585-602, December.
    3. Lucie Dostál & Siegfried Gabler & Matthias Ganninger & Ralf Münnich, 2016. "Frame Correction Modelling with Applications to the German Register-Assisted Census 2011," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 904-920, September.
    4. Luna Angela & Zhang Li-Chun & Whitworth Alison & Piller Kirsten, 2015. "Small Area Estimates of the Population Distribution by Ethnic Group in England: A Proposal Using Structure Preserving Estimators," Statistics in Transition New Series, Polish Statistical Association, vol. 16(4), pages 585-602, December.
    5. Jiming Jiang & P. Lahiri, 2006. "Mixed model prediction and small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-96, June.
    6. María Dolores Esteban & María José Lombardía & Esther López-Vizcaíno & Domingo Morales & Agustín Pérez, 2023. "Small area estimation of average compositions under multivariate nested error regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 651-676, June.
    7. María Dolores Esteban & María José Lombardía & Esther López-Vizcaíno & Domingo Morales & Agustín Pérez, 2020. "Small area estimation of proportions under area-level compositional mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 793-818, September.
    8. Berg, Emily J. & Fuller, Wayne A., 2012. "Estimators of error covariance matrices for small area prediction," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2949-2962.
    9. Suesse Thomas & Namazi-Rad Mohammad-Reza & Mokhtarian Payam & Barthélemy Johan, 2017. "Estimating Cross-Classified Population Counts of Multidimensional Tables: An Application to Regional Australia to Obtain Pseudo-Census Counts," Journal of Official Statistics, Sciendo, vol. 33(4), pages 1021-1050, December.
    10. Hormoz SOHRABI, 2018. "Adaptive k-tree sample plot for the estimation of stem density: An empirical approach," Journal of Forest Science, Czech Academy of Agricultural Sciences, vol. 64(1), pages 17-24.
    11. Thomas Zimmermann, 2019. "Einsatzmöglichkeiten von Small Area-Verfahren bei Kohortenschätzungen im Zensus 2021 [Applicablity of small area estimation methods for demographic cohorts in the Census 2021]," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 13(2), pages 157-177, September.

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