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<p>We consider a small area estimation model under square-root transformation in the presence of functional measurement error. When measurement error is present, the Bayes predictor can no longer be used as it depends on the covariates even if parameters are known. Therefore suitable replacements are called for, and we propose a predictor that only depends on observed responses and data obtained from a large secondary survey. Moreover, some estimation methods of unknown parameters are considered. In the simulations section, we evaluate the performance using the mean squared prediction error (MSPE) and discuss several scenarios in terms of the number of areas and the sample sizes in a large secondary survey.</p>

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Small Area Estimation under Square Root Transformed Fay-Herriot Model with Functional Measurement Error in Covariates

  • 期刊论文

  • 发表日期：

    2025年5月21日

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  • Ka Long Keith Ho,
  • Masayo Y. Hirose,
  • Malay Ghosh,
  • Kimiyo Kikuchi

摘要

We consider a small area estimation model under square-root transformation in the presence of functional measurement error. When measurement error is present, the Bayes predictor can no longer be used as it depends on the covariates even if parameters are known. Therefore suitable replacements are called for, and we propose a predictor that only depends on observed responses and data obtained from a large secondary survey. Moreover, some estimation methods of unknown parameters are considered. In the simulations section, we evaluate the performance using the mean squared prediction error (MSPE) and discuss several scenarios in terms of the number of areas and the sample sizes in a large secondary survey.