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On Accuracy Estimation Using Parametric Bootstrap in small Area Prediction Problems

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  • Żądło Tomasz

    (University of Economics in Katowice, Department of Statistics, Econometrics and Mathematics, 50, 1 Maja Street, 40-287Katowice, Poland.)

Abstract

We consider longitudinal data and the problem of prediction of subpopulation (domain) characteristics that can be written as a linear combination of the variable of interest, including cases of small or zero sample sizes in the domain and time period of interest. We consider the empirical version of the predictor proposed by Royall (1976) showing that it is a generalization of the empirical version of the predictor presented by Henderson (1950). We propose a parametric bootstrap MSE estimator of the predictor. We prove its asymptotic unbiasedness and derive the order of its bias. Considerations are supported by Monte Carlo simulation analyses to compare its accuracy (not only the bias) with other MSE estimators, including jackknife and weighted jackknife MSE estimators that we adapt for the considered predictor.

Suggested Citation

  • Żądło Tomasz, 2020. "On Accuracy Estimation Using Parametric Bootstrap in small Area Prediction Problems," Journal of Official Statistics, Sciendo, vol. 36(2), pages 435-458, June.
    • Handle: RePEc:vrs:offsta:v:36:y:2020:i:2:p:435-458:n:7
    DOI: 10.2478/jos-2020-0022
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    References listed on IDEAS

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    1. Tomáš Hobza & Domingo Morales & Laureano Santamaría, 2018. "Small area estimation of poverty proportions under unit-level temporal binomial-logit mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 270-294, June.
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