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On the choice of the number of Monte Carlo iterations and bootstrap replicates in Empirical Best Prediction

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  • Chwila Adam

    (University of Economics in Katowice, Katowice, Poland)

  • Żądło Tomasz

    (University of Economics in Katowice, Katowice, Poland)

Abstract

Empirical Best Predictors (EBPs) are widely used for small area estimation purposes. In the case of longitudinal surveys, this class of predictors can be used to predict any given population or subpopulation characteristic for any time period, including future periods. Generally, the value of an EBP is computed by means of Monte Carlo algorithms, while its MSE is usually estimated using the parametric bootstrap method. Model-based simulation studies of the properties of the predictors require numerous repetitions of the random generation of population data. This leads to a question about the dependence between the number of iterations in all the procedures and the stability of the results. The aim of the paper is to show this dependence and to propose methods of choosing the appropriate number of iterations in practice, using a set of real economic longitudinal data available at the United States Census Bureau website.

Suggested Citation

  • Chwila Adam & Żądło Tomasz, 2020. "On the choice of the number of Monte Carlo iterations and bootstrap replicates in Empirical Best Prediction," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 35-60, June.
    • Handle: RePEc:vrs:stintr:v:21:y:2020:i:2:p:35-60:n:5
    DOI: 10.21307/stattrans-2020-013
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    References listed on IDEAS

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    1. Berg, Emily & Chandra, Hukum, 2014. "Small area prediction for a unit-level lognormal model," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 159-175.
    2. Nikos Tzavidis & Li‐Chun Zhang & Angela Luna & Timo Schmid & Natalia Rojas‐Perilla, 2018. "From start to finish: a framework for the production of small area official statistics," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 927-979, October.
    3. Miguel Boubeta & María José Lombardía & Domingo Morales, 2016. "Empirical best prediction under area-level Poisson mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 548-569, September.
    4. Boubeta, Miguel & Lombardía, María José & Morales, Domingo, 2017. "Poisson mixed models for studying the poverty in small areas," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 32-47.
    5. Rudolf Beran, 1997. "Diagnosing Bootstrap Success," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 1-24, March.
    6. Guadarrama, María & Molina, Isabel & Rao, J.N.K., 2018. "Small area estimation of general parameters under complex sampling designs," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 20-40.
    7. Mamadou S. Diallo & J. N. K. Rao, 2018. "Small area estimation of complex parameters under unit‐level models with skew‐normal errors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(4), pages 1092-1116, December.
    8. Sumonkanti Das & Stephen Haslett, 2019. "A Comparison of Methods for Poverty Estimation in Developing Countries," International Statistical Review, International Statistical Institute, vol. 87(2), pages 368-392, August.
    9. Donald W. K. Andrews & Moshe Buchinsky, 2000. "A Three-Step Method for Choosing the Number of Bootstrap Repetitions," Econometrica, Econometric Society, vol. 68(1), pages 23-52, January.
    10. Peter Hall & Tapabrata Maiti, 2006. "On parametric bootstrap methods for small area prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 221-238, April.
    11. Donald W.K. Andrews & Moshe Buchinsky, 1997. "On the Number of Bootstrap Repetitions for Bootstrap Standard Errors, Confidence Intervals, and Tests," Cowles Foundation Discussion Papers 1141R, Cowles Foundation for Research in Economics, Yale University.
    12. Andrews, Donald W. K. & Buchinsky, Moshe, 2001. "Evaluation of a three-step method for choosing the number of bootstrap repetitions," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 345-386, July.
    13. Jiming Jiang & P. Lahiri, 2001. "Empirical Best Prediction for Small Area Inference with Binary Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 217-243, June.
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