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Small Area Estimation of Proportions with Constraint for National Resources Inventory Survey

Author

Listed:
  • Xin Wang

    (Miami University)

  • Emily Berg

    (Iowa State University)

  • Zhengyuan Zhu

    (Iowa State University)

  • Dongchu Sun

    (University of Missouri-Columbia
    East China Normal University)

  • Gabriel Demuth

    (Iowa State University)

Abstract

Motivated by the need to produce small area estimates for the National Resources Inventory survey, we develop a spatial hierarchical model based on the generalized Dirichlet distribution to construct small area estimators of compositional proportions in several mutually exclusive and exhaustive landcover categories. At the observation level, the standard design-based estimators of the proportions are assumed to follow the generalized Dirichlet distribution. After proper transformation of the design-based estimators, beta regression is applicable. We consider a logit mixed model for the expectation of the beta distribution, which incorporates covariates through fixed effects and spatial effect through a conditionally autoregressive process. In a design-based evaluation study, the proposed model-based estimators are shown to have smaller root-mean-square error and relative root-mean-square error than design-based estimators and multinomial model-based estimators. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • Xin Wang & Emily Berg & Zhengyuan Zhu & Dongchu Sun & Gabriel Demuth, 2018. "Small Area Estimation of Proportions with Constraint for National Resources Inventory Survey," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(4), pages 509-528, December.
    • Handle: RePEc:spr:jagbes:v:23:y:2018:i:4:d:10.1007_s13253-018-0329-6
    DOI: 10.1007/s13253-018-0329-6
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    References listed on IDEAS

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    1. Tapabrata Maiti & Hao Ren & Samiran Sinha, 2014. "Prediction Error of Small Area Predictors Shrinking Both Means and Variances," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 775-790, September.
    2. Isabel Molina & Ayoub Saei & M. José Lombardía, 2007. "Small area estimates of labour force participation under a multinomial logit mixed model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(4), pages 975-1000, October.
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    Cited by:

    1. Wang, Xin & Zhu, Zhengyuan & Zhang, Hao Helen, 2023. "Spatial heterogeneity automatic detection and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    2. Hao Sun & Emily Berg & Zhengyuan Zhu, 2022. "Bivariate small‐area estimation for binary and gaussian variables based on a conditionally specified model," Biometrics, The International Biometric Society, vol. 78(4), pages 1555-1565, December.

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