References
- Białek, J. 2014. “Simulation study of an original price index formula.” Communications in Statistics - Simulation and Computation 43: 285–297. DOI: http://doi.org/10.1080/03610918.2012.700367.10.1080/03610918.2012.700367
- Butar, F.B. and P. Lahiri. 2003. “On measures of uncertainty of empirical Bayes small-area estimators.” Journal of Statistical Planning and Inference 112: 63–76. DOI: http://doi.org/10.1016/S0378-3758(02)00323-3.10.1016/S0378-3758(02)00323-3
- Chen, S. and P. Lahiri, 2002. “A weighted jackknife MSPE estimator in small-area estimation.” In Proceedings of the Section on Survey Research Methods: American Statistical Association, May 14–19, 2002: 473–477. Florida, VAL: American Statistical Association. Available at: http://www.asasrms.org/Proceedings/y2002/Files/JSM2002-001127.pdf (accessed January 2020).
- Chen, S. and P. Lahiri. 2003. “A comparison of different MSPE estimators of EBLUP for the Fay-Herriot model.” In Proceedings of the Section on Survey Research Methods: American Statistical Association, May 15–18, 2003: 905–911. Nashville, VAL: American Statistical Association. Available at: http://www.asasrms.org/Proceedings/y2003/Files/JSM2003-000585.pdf (accessed January 2020).
- D’Aló, M., S. Falorsi, and F. Solari. 2017. “Space-Time Unit-Level EBLUP for Large Data Sets.” Journal of Official Statistics 33: 61–77. DOI: http://doi.org/10.1515/jos-2017-0004.10.1515/jos-2017-0004
- Das, K., J. Jiang, and J.N.K. Rao. 2004. “Mean squared error of empirical predictor.” The Annals of Statistics 32: 818–840. DOI: http://doi.org/10.1214/009053604000000201.10.1214/009053604000000201
- Datta, G.S. and P. Lahiri. 2000. “A unified measure of uncertainty of estimated best linear unbiased predictors in small area estimation problems.” Statistica Sinica 10: 613–627. Available at: http://www3.stat.sinica.edu.tw/statistica/oldpdf/A10n214.pdf (accessed January 2020).
- Fabrizi, E., M.R. Ferrante, and S. Pacei. 2007. “Small area estimation of average household income based on unit level models for panel data.” Survey Methodology 33: 187–198. Available at: https://www150.statcan.gc.ca/n1/en/pub/12-001-x/2007002/article/10496-eng.pdf?st=eifh–iS (accessed January 2020).
- González-Manteiga, W., M.J. Lombardía, I. Molina, D. Morales, and L. Santamaría. 2007. “Estimation of the mean squared error of predictors of small area linear parameters under a logistic mixed model.” Computational Statistics and Data Analysis 51: 2720–2733. DOI: http://doi.org/10.1016/j.csda.2006.01.012.10.1016/j.csda.2006.01.012
- González-Manteiga, W., M.J. Lombardía, I. Molina, D. Morales, and L. Santamaría. 2008. “Bootstrap mean squared error of small-area EBLUP.” Journal of Statistical Computation and Simulation 78: 443 – 462. DOI: http://doi.org/10.1080/00949650601141811.10.1080/00949650601141811
- Harville, D.A. and D.R. Jeske. 1992. “Mean square error of estimation or prediction under general linear model.” Journal of Statistical Computation and Simulation 87: 724–731. DOI: http://doi.org/10.1080/01621459.1992.10475274.10.1080/01621459.1992.10475274
- Henderson, C.R. 1950. “Estimation of genetic parameters (Abstract).” Annals of Mathematical Statistics 21: 309–310.
- Hobza, T. and D. Morales. 2013. “Small area estimation under random regression coefficient models.” Journal of Statistical Computation and Simulation 83: 2160–2177. DOI: http://doi.org/10.1080/00949655.2012.684094.10.1080/00949655.2012.684094
- Hobza, T., D. Morales, and L. Santamaría. 2018. “Small area estimation of poverty proportions under unit-level temporal binomial-logit mixed models.” TEST 27: 270–294. DOI: http://doi.org/10.1007/s11749-017-0545-3.10.1007/s11749-017-0545-3
- Jiang, J. 1996. “REML Estimation: Asymptotic Behavior and Related Topics.” The Annals of Statistics 24: 255–286. DOI: http://doi.org/10.1214/aos/1033066209.10.1214/aos/1033066209
- Jiang, J. and P. Lahiri. 2006. “Mixed model prediction and small area estimation.” Test 15: 1–96. DOI: http://doi.org/10.1007/BF02595419.10.1007/BF02595419
- Jiang, J., P. Lahiri, and S.-M. Wan. 2002. “Unified jackknife theory for empirical best prediction with M-estimation.” The Annals of Statistics 30: 1782–1810. DOI: http://doi.org/10.1214/aos/1043351257.10.1214/aos/1043351257
- Kackar, R.N. and D.A. Harville. 1981. “Unbiasedness of two-stage estimation and prediction procedures for mixed linear models.” Communications in Statistics, Ser. A 10: 1249–1261. DOI: http://doi.org/10.1080/03610928108828108.10.1080/03610928108828108
- Kackar, R.N. and D.A. Harville. 1984. “Approximations for standard errors of estimators of fixed and random effects in mixed linear models.” Journal of the American Statistical Association 79: 853–862. DOI: http://doi.org/10.1080/01621459.1984.10477102.10.1080/01621459.1984.10477102
- Marhuenda, Y., I. Molina, and D. Morales. 2013. “Small area estimation with spatio-temporal Fay-Herriot models.” Computational Statistics & Data Analysis 58: 308–325. DOI: http://doi.org/10.1016/j.csda.2012.09.002.10.1016/j.csda.2012.09.002
- Molina, I., D. Morales, M. Pratesi, and N. Tzavidis. eds. 2010. “Final small area estimation developments and simulation results.” SAMPLE project: Small Area Methods for Poverty and Living Conditions Estimates. http://www.sample-project.eu/images/stories/docs/samplewp2d12%2616_saefinal.pdf (accessed January 2020).
- Moura, F.A.S. and D. Holt. 1999. “Small area estimation using multilevel models.” Survey Methodology 25: 73–80.
- Morales, D. and L. Santamaría. 2019. “Small area estimation under unit-level temporal linear mixed models.” Journal of Statistical Computation and Simulation. 89: 1592–1620. DOI: http://doi.org/10.1080/00949655.2019.1590578.10.1080/00949655.2019.1590578
- Muirhead, R.J. 2005. Aspects of Multivariate Statistical Theory. New Jersey: John Wiley & Sons.
- Nissinen, K. 2009. Small area estimation with linear mixed models for unit-level panel and rotating panel data. Dissertation, University of Jyväskylä.
- Pagliarella, M.C. and R. Salvatore. 2016. “Unit Level Spatio-temporal Models.” In Analysis of Poverty Data by Small Area Estimation, edited by M. Pratesi, 227–243. Chichester: Wiley.10.1002/9781118814963.ch12
- Prasad, N.G.N. and J.N.K. Rao. 1990. “The estimation of mean the mean squared error of small-area-estimators.” Journal of the American Statistical Association 85: 163–171. DOI: http://doi.org/10.1080/01621459.1990.10475320.10.1080/01621459.1990.10475320
- R Core Team. 2019. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. Available at: https://www.R-project.org/ (accessed January 2020).
- Rao, J.N.K. and I. Molina. 2015. Small area estimation. Second edition. New Jersey: Wiley.10.1002/9781118735855
- Rao, J.N.K. and M. Yu. 1994. “Small area estimation by combining time-series and cross-sectional data.” Canadian Journal of Statistics 22: 511–528. DOI: http://doi.org/10.2307/3315407.10.2307/3315407
- Robinson, G.K. 1991. “That BLUP is a good thing: the estimation of random effects.” Statistical Science 6: 15–51. DOI: http://doi.org/10.1214/ss/1177011926.10.1214/ss/1177011926
- Royall, R.M. 1976. “The linear least squares prediction approach to two-stage sampling.” Journal of the American Statistical Association 71: 657–473. DOI: http://doi.org/10.1080/01621459.1976.10481542.10.1080/01621459.1976.10481542
- Saei, A. and R. Chambers. 2003. Small Area Estimation Under Linear and Generalized Linear Mixed Models with Time and Area Effects. S3RI, Methodology Working Paper M03/15r, Southampton: University of Southampton. Available at: https://eprints.soton.ac.uk/8165/1/8165-01.pdf (accessed January 2020).
- Schmid, T. and R. Münnich. 2014. “Spatial robust small area estimation.” Statistical Papers 55: 653–670. DOI: http://doi.org/10.1007/s00362-013-0517-y.10.1007/s00362-013-0517-y
- Stukel, D.M. and J.N.K. Rao. 1999. “On small-area estimation under two-fold nested error regression models.” Journal of Statistical Planning and Inference 78: 131–147. DOI: http://doi.org/10.1016/S0378-3758(98)00211-0.10.1016/S0378-3758(98)00211-0
- Vaida, F. and S. Blanchard. 2005. “Conditional Akaike Information for Mixed-Effects Models.” Biometrika 92: 351–370. DOI: http://doi.org/10.1093/biomet/92.2.351.10.1093/biomet/92.2.351
- Valliant, R., A.H. Dorfman, and R.M. Royall. 2000. Finite population sampling and inference. A prediction approach. New York: John Wiley & Sons.
- Verbeke, G. and G. Molenberghs. 2000. Linear mixed models for longitudinal data. New York: Springer-Verlag.10.1007/978-1-4419-0300-6
- Żądło, T. 2004. “On unbiasedness of some EBLU predictor.” In Proceedings in Computational Statistics 2004, Physica-Verlag, Heidelberg-New York, August 23–27, 2004. 2019–2026. Prague, VAL: International Association for Statistical Computing. Available at: https://link.springer.com/book/10.1007/978-3-7908-2656-2 (accessed January 2020).
- Żądło, T. 2009. “On MSE of EBLUP.” Statistical Papers 50: 101–118. DOI: http://doi.org/10.1007/s00362-007-0066-3.10.1007/s00362-007-0066-3
- Żądło, T. 2014. “On the Prediction of the Subpopulation Total Based on Spatially Correlated Longitudinal Data.” Mathematical Population Studies 21: 30–44. DOI: http://doi.org/10.1080/08898480.2013.836387.10.1080/08898480.2013.836387
- Żądło, T. 2015a. “On longitudinal moving average model for prediction of subpopulation total.” Statistical Papers 56: 749–771. DOI: http://doi.org/10.1007/s00362-014-0607-5.10.1007/s00362-014-0607-5
- Żądło, T. 2015b. “On prediction for correlated domains in longitudinal surveys.” Communications in Statistics - Theory and Methods 44: 683–697. DOI: http://doi.org/10.1080/03610926.2013.857867.10.1080/03610926.2013.857867