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Observed best selective prediction in small area estimation

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  • Sugasawa, Shonosuke
  • Kawakubo, Yuki
  • Datta, Gauri Sankar

Abstract

In small area estimation methodology, selection of the suitable covariates and estimation in the selected model are usually considered separately. In this paper, we consider variable selection and estimation simultaneously to minimize the total mean squared prediction errors (MSPE) for estimation of small area means. The derived method, which we call observed best selective prediction (OBSP), can be regarded as an extension of the observed best prediction (OBP) method by Jiang et al. (2011). When the true model is included in the largest model, the resulting OBSP estimator is consistent. Based on the asymptotic result, we derive an estimator of MSPE by applying the parametric bootstrap method. Through simulation experiments, we investigate the finite-sample performance of OBSP together with OBP in which the variable selection is carried out by using AIC and BIC, and OBP using all the covariates. As an example, we applied OBSP to Japanese survey data.

Suggested Citation

  • Sugasawa, Shonosuke & Kawakubo, Yuki & Datta, Gauri Sankar, 2019. "Observed best selective prediction in small area estimation," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 383-392.
    • Handle: RePEc:eee:jmvana:v:173:y:2019:i:c:p:383-392
    DOI: 10.1016/j.jmva.2019.04.002
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    References listed on IDEAS

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    1. Gauri Sankar Datta & J. N. K. Rao & David Daniel Smith, 2005. "On measuring the variability of small area estimators under a basic area level model," Biometrika, Biometrika Trust, vol. 92(1), pages 183-196, March.
    2. Gauri Datta & Tatsuya Kubokawa & Isabel Molina & J. Rao, 2011. "Estimation of mean squared error of model-based small area estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 367-388, August.
    3. Peide Shi & Chih‐Ling Tsai, 2002. "Regression model selection—a residual likelihood approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 237-252, May.
    4. Florin Vaida & Suzette Blanchard, 2005. "Conditional Akaike information for mixed-effects models," Biometrika, Biometrika Trust, vol. 92(2), pages 351-370, June.
    5. Jiang, Jiming & Nguyen, Thuan & Rao, J. Sunil, 2011. "Best Predictive Small Area Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 732-745.
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    Cited by:

    1. Tomasz .Zk{a}d{l}o & Adam Chwila, 2024. "A step towards the integration of machine learning and small area estimation," Papers 2402.07521, arXiv.org.

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