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Żądło (2012) proposed a certain unit-level longitudinal model which was a special case of the General Linear Mixed Model. Two vectors of random components included in the model obey assumptions of simultaneous spatial autoregressive process (SAR) and temporal first-order autoregressive process (AR(1)) respectively. Moreover, it is assumed that the population can change in time and the population elements can change its domains' (subpopulations') affiliation in time. Under the proposed model, Żądło (2012) derived the Empirical Best Linear Unbiased Predictor (EBLUP) of the domain total. What is more (based on the theorem proved by Żądło (2009)), the approximate equation of the mean squared error (MSE) was derived and its estimator based on the Taylor approximation was proposed. The proposed MSE estimator was derived under some assumptions including that the variance-covariance matrix can be decomposed into linear combination of variance components. The assumption was not met under the proposed model. In the paper the jackknife MSE estimator for the derived EBLUP will be proposed based on the results presented by Jiang, Lahiri, Wan (2002). The bias of the jackknife MSE estimator will be compared in the simulation study with the bias of the MSE estimator based on the Taylor approximation.(original abstract)
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- Uniwersytet Ekonomiczny w Katowicach
Bibliografia
- Datta G.S., Lahiri P. (2000). A unified measure of uncertainty of estimated best linear unbiased predictors in small area estimation problems. Statistica Sinica 10. Pp. 613-627.
- Jiang J., Lahiri P., Wan S.-M. (2002). A unified jackknife theory for empirical best prediction with M-estimation. The Annals of Statistics. Vol. 30. No 6. Pp. 1782-1810.
- R Development Core Team (2012). A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna.
- Royall R.M. (1976). The linear least squares prediction approach to two-stage sampling. Journal of the American Statistical Association 71. Pp. 657-473.
- Żądło T (2004). On unbiasedness of some EBLU predictor. In: J. Antoch (ed). Proceedings in Computational Satistics 2004. Heidelberg-New York. Physica-Verlag. Pp. 2019-2026.
- Żądło T. (2009). On MSE of EBLUP. Statistical Papers 50. Pp. 101-118.
- Żądło T. (2014). On the prediction of the subpopulation total based on spatially correlated longitudinal data. Mathematical Population Studies 21. Pp. 30-44.
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Bibliografia
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