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Bayesian Curve-Fitting in Semiparametric Small Area Models with Measurement Errors

  • Hwang, Jinseub (National Evidence-based Healthcare Collaborating Agency) ;
  • Kim, Dal Ho (Department of Statistics, Kyungpook National University)
  • Received : 2015.04.20
  • Accepted : 2015.07.04
  • Published : 2015.07.31

Abstract

We study a semiparametric Bayesian approach to small area estimation under a nested error linear regression model with area level covariate subject to measurement error. Consideration is given to radial basis functions for the regression spline and knots on a grid of equally spaced sample quantiles of covariate with measurement errors in the nested error linear regression model setup. We conduct a hierarchical Bayesian structural measurement error model for small areas and prove the propriety of the joint posterior based on a given hierarchical Bayesian framework since some priors are defined non-informative improper priors that uses Markov Chain Monte Carlo methods to fit it. Our methodology is illustrated using numerical examples to compare possible models based on model adequacy criteria; in addition, analysis is conducted based on real data.

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