A Varying Coefficients Model For Estimating Finite Population Totals: A Hierarchical Bayesian Approach

  • Ciro Velasco-CruzEmail author
  • Luis Fernando Contreras-Cruz
  • Eric P. Smith
  • José E. Rodríguez


In some finite sampling situations, there is a primary variable that is sampled, and there are measurements on covariates for the entire population. A Bayesian hierarchical model for estimating totals for finite populations is proposed. A nonparametric linear model is assumed to explain the relationship between the dependent variable of interest and covariates. The regression coefficients in the linear model are allowed to vary as a function of a subset of covariates nonparametrically based on B-splines. The generality of this approach makes it robust and applicable to data collected using a variety of sampling techniques, provided the sample is representative of the finite population. A simulation study is carried out to evaluate the performance of the proposed model for the estimation of the population total. Results indicate accurate estimation of population totals using the approach. The modeling approach is used to estimate the total production of avocado for a large group of groves in Mexico.


Bayesian hierarchical model Population total Varying coefficient model Auxiliary information Nonparametric regression model 


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Copyright information

© International Biometric Society 2016

Authors and Affiliations

  • Ciro Velasco-Cruz
    • 1
    Email author
  • Luis Fernando Contreras-Cruz
    • 2
  • Eric P. Smith
    • 3
  • José E. Rodríguez
    • 4
  1. 1.Statistics ProgramColegio de PostgraduadosMexicoMexico
  2. 2.Departamento de FitotécniaUniversidad Autónoma ChapingoTexcocoMexico
  3. 3.Department of StatisticsVirginia TechBlacksburgUSA
  4. 4.Universidad de GuanajuatoGuanajuatoMexico

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