On the Simulation Study of Jackknife and Bootstrap MSE Estimators of a Domain Mean Predictor for Fay‑Herriot Model
DOI:
https://doi.org/10.18778/0208-6018.331.11Keywords:
estimators of MSE, jackknife, parametric bootstrap, Empirical Best Linear Unbiased Predictor, Fay‑Herriot model, simulationAbstract
We consider the problem of the estimation of the mean squared error (MSE) of some domain mean predictor for Fay‑Herriot model. In the simulation study we analyze properties of eight MSE estimators including estimators based on the jackknife method (Jiang, Lahiri, Wan, 2002; Chen, Lahiri, 2002; 2003) and parametric bootstrap (Gonzalez‑Manteiga et al., 2008; Buthar, Lahiri, 2003). In the standard Fay‑Herriot model the independence of random effects is assumed, and the biases of the MSE estimators are small for large number of domains. The aim of the paper is the comparison of the properties of MSE estimators for different number of domains and the misspecification of the model due to the correlation of random effects in the simulation study.
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References
Bell W. (1997), Models for county and state poverty estimates. Preprint, Statistical Research Division, U.S. Census Bureau.
Google Scholar
Bell W. (2001), Discussion with “Jackknife in the Fay‑Herriot Model with An Example”, “Proc. of the Seminar of Funding Opportunity in Survey Research”, pp. 98–104.
Google Scholar
Butar F.B., Lahiri P. (2003), On Measures of Uncertainty of Empirical Bayes Small‑Area Estimators, “Journal of Statistical Planning and Inference”, vol. 112, pp. 635–676.
Google Scholar
Chatterjee S., Lahiri P., Li H. (2008), Parametric Bootstrap Approximation to the Distribution of EBLUP and Related Prediction Intervals in Linear Mixed Models, “The Annals of Statistics”, vol. 36, no. 3, pp. 1221–1245.
Google Scholar
Chen S., Lahiri P. (2002), A Weighted Jackknife MSPE Estimator in Small‑Area Estimation, “Proceeding of the Section on Survey Research Methods”, American Statistical Association, pp. 473–477.
Google Scholar
Chen S., Lahiri P. (2003), A Comparison of Different MSPE Estimators of EBLUP for the Fay‑Herriot Model, “Proceeding of the Section on Survey Research Methods”, American Statistical Association, pp. 905–911.
Google Scholar
Conley T.G. (1999), GMM estimation with cross selection dependence, “Journal of Econometrics”, vol. 92(1), pp. 1–45.
Google Scholar
Dacey M. (1968), A review of measures of contiguity for two and k‑color maps, [in:] B. Berry, D. Marble (eds.), Spatial analysis: A Reader in Statistical Geography, Prentice Hall, Englewood Cliffs.
Google Scholar
Datta G., Lahiri P. (2000), A unified measure of uncertainty of estimated best linear unbiased predictors in small area estimation problems, “Statistica Sinica”, vol. 10, pp. 613–627.
Google Scholar
Datta G.S., Rao J.N.K., Smith D.D. (2005), On Measuring the Variability of Small Area Estimators under a Basic Area Level Model, “Biometrica”, vol. 92, pp. 183–196.
Google Scholar
Fay R.E. III, Herriot R.A. (1979), Estimation of Incomes for Small Places: An Application of James‑Stein Procedures to Census Data, “Journal of the American Statistical Association”, vol. 74, pp. 269–277, http://dx.doi.org/10.2307/2286322.
Google Scholar
Gonzales‑Manteiga W., Lombardia M., Molina I., Morales D., Santamaria L. (2008), Bootstrap Mean Squared Error of Small‑Area EBLUP, “Journal of Statistical Computation and Simulation”, vol. 78, pp. 433–462, http://dx.doi.org/10.1007/s00180-008-0138-4.
Google Scholar
Henderson C.R. (1950), Estimation of genetic parameters (Abstracts), “Annals of Mathematical Statistics”, vol. 21, pp. 309–310.
Google Scholar
Jędrzejczak A. (2011), Metody analizy rozkładów dochodów i ich koncentracji, Wydawnictwo Uniwersytetu Łódzkiego, Łódź.
Google Scholar
Jiang J. (2007), Linear and Generalized Linear Mixed Models and Their Applications, Springer Science+Business Media, New York.
Google Scholar
Jiang J., Lahiri P. (2006), Mixed Model Prediction and Small Area Estimation, “Test”, vol. 15, no. 1, pp. 1–96, http://dx.doi.org/10.1007/BF02595419.
Google Scholar
Jiang J., Lahiri P., Wan S.‑M. (2002), Unified Jackknife Theory for Empirical Best Prediction with M‑estimation, “The Annals of Statistics”, vol. 30, pp. 1782–1810.
Google Scholar
Kackar R.N., Harville D.A. (1981), Unbiasedness of two‑stage estimation prediction procedures for mixed linear models, “Communications in Statistics”, Series A, vol. 10, pp. 1249–1261.
Google Scholar
Kackar R.N., Harville D.A. (1984), Approximations for Standard Errors of Estimators of Fixed and Random Effect in Mixed Linear Models, “Journal of the American Statistical Association”, vol. 79, pp. 853–862.
Google Scholar
Karpuk M. (2015), Wpływ czynników przestrzennych na ruch turystyczny w województwie zachodniopomorskim (2006–2012), “Zeszyty Naukowe Wydziału Nauk Ekonomicznych Politechniki Koszalińskiej”, vol. 19, pp. 39–56.
Google Scholar
Krzciuk M.K. (2015), On the simulation study of the properties of MSE estimators in small area statistics, Conference Proceedings. 33rd International Conference Mathematical Methods in Economics 2015, pp. 413–418.
Google Scholar
Kuc M. (2015), Wpływ sposobu definiowania macierzy wag przestrzennych na wynik porządkowania liniowego państw Unii Europejskiej pod względem poziomu życia ludności, “Taksonomia 24”, vol. 384, pp. 163–170.
Google Scholar
Lahiri P. (2003), On the Impact of Bootstrap in Survey Sampling and Small‑Area Estimation, “Statistical Science”, vol. 18, no. 2, pp. 199–210.
Google Scholar
Lohr S.L., Rao J.N.K. (2009), Jackknife estimation of mean squared error of small area predictors in nonlinear mixed models, “Biometrika”, vol. 96, pp. 457–468.
Google Scholar
Molina I., Rao J. (2010), Small Area Estimation of Powerty indicators, “The Canadian Journal of Statistics”, vol. 38, no. 3, pp. 369–385.
Google Scholar
Prasad N.G.N., Rao J.N.K. (1990), The Estimation of the Mean Squared Error of Small‑Area Estimators, “Journal of the American Statistical Association”, vol. 85, no. 409, pp. 163–171, http://dx.doi.org/10.2307/2289539.
Google Scholar
Pietrzak M.B. (2010), Dwuetapowa procedura budowy przestrzennej macierzy wag z uwzględnieniem odległości ekonomicznej, “Oeconomia Copernicana”, vol. 1, pp. 65–78.
Google Scholar
Pratesi M., Salvati N. (2008), Small Area Estimation: The EBLUP Estimator Based on Spatially Correlated Random Area Effects, “Statistical Methods and Applications”, vol. 17, pp. 113–141, http://dx.doi.org/10.1007/s10260-007-0061-9.
Google Scholar
Rao J.N.K. (2003), Small Area Estimation, John Wiley & Sons, Hoboken.
Google Scholar
Rao J.N.K., You Y. (1994), Small Area Estimation by Combining Time‑Series and Cross‑Sectional Data, “Canadian Journal of Statistics”, vol. 22, pp. 511–528.
Google Scholar
R Development Core Team (2016), A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna.
Google Scholar
Rao J.N.K., Molina I. (2015), Small Area Estimation, John Wiley & Sons, Hoboken.
Google Scholar
Rueda C., Mendez J.A., Gomez F. (2010), Small Area Estimators on Restricted Mixed Models, “Sociedad de Estadística e Investigación Operativa”, vol. 16, pp. 558–579, http://dx.doi.org/10.1007/s11749-010-0186-2.
Google Scholar
Slud E.V., Maiti T. (2006), Mean‑Squared Error Estimation in Transformed Fay‑Herriot Models, “Journal of the Royal Statistical Society. Series B (Statistical Methodology)”, vol. 68, pp. 239–257.
Google Scholar
Suchecki B. (2010), Ekonometria przestrzenna. Metody i modele analizy danych przestrzennych, C.H. Beck, Warszawa.
Google Scholar
Wang J., Fuller W.A. (2003), The Mean Squared Error of Small Area Predictors Constructed with Estimated Area Variances, “Journal of the American Statistical Association”, vol. 98, pp. 716–723.
Google Scholar
Wolter K.M. (1985), Introduction to variance estimation, Springer‑Verlag, New York.
Google Scholar
Żądło T. (2009), On prediction of the domain total under some special case of type A general Linear Mixed Models, “Folia Oeconomica”, vol. 228, pp. 105–112.
Google Scholar
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