Parametric bootstrap mean squared error of a small area multivariate EBLUP

References

• Baillo, A., and I. Molina. 2009. Mean squared errors of small-area estimators under a unit-level multivariate model. Statistics 43:553–569.
   Web of Science ®Google Scholar
• Battese, G. E., R. M. Harter, and W. A. Fuller. 1988. An error-components model for prediction of county crop areas using survey and satellite data. Journal of the American Statistical Association 83 (401):28–36.
   Web of Science ®Google Scholar
• Box, G. E. P., and D. R. Cox. 1964. An analysis of transformations. Journal of Royal Statistical Society Series B 26:211–246.
   Google Scholar
• Chambers, R., H. Chandra, and N. Tzavidis. 2011. On bias-robust mean squared error estimation for pseudo-linear small area estimators. Survey Methodology 37:153–170.
   Web of Science ®Google Scholar
• Das, K., J. Jiang, and J. N. K. Rao. 2004. Mean squared error of empirical predictor. Annals of Statistics 32:818–840.
   Web of Science ®Google Scholar
• Datta, G. S., B. Day, and I. Basawa. 1999. Empirical best linear unbiased and empirical Bayes prediction in multivariate small area estimation. Journal of Statistical Planning and Inference 75:269–279.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Efron, B., and R. Tibshirani. 1993. An introduction to the bootstrap. London: Chapman and Hall.
   Google Scholar
• Fuller, W. A., and R. M. Harter. 1987. The multivariate components of variance model for small area estimation. In Small area statistics, ed. by R. Platek, J. N. K. Rao, C. E. Sarndal, and M. P. Singh, 103–123. New York: Wiley.
   Google Scholar
• González-Manteiga, W., M. J. Lombardía, I. Molina, D. Morales, and L. Santamaría. 2008a. Bootstrap mean squared error of a small-area EBLUP. Journal of Statistical Computation and Simulation 78:443–462.
   Web of Science ®Google Scholar
• González-Manteiga, W., M. J. Lombardía, I. Molina, D. Morales, and L. Santamaría. 2008b. Analytic and bootstrap approximations of prediction errors under multivariate Fay-Herriot model. Computational Statistics and Data Analysis 52:5242–5252.
   Web of Science ®Google Scholar
• Giusti, C., N. Tzavidis, M. Pratesi, and N. Salvati. 2013. Resistance to outliers of M-Quantile and robust random effects small area models. Communications in Statistics – Simulation and Computation 43:549–568.
   Web of Science ®Google Scholar
• Hall, P. 1992. The bootstrap and edgeworth expansion. New York, NY: Springer.
   Google Scholar
• Hall, P., and T. Maiti. 2006. Nonparametric estimation of mean-squared prediction error in nested-error regression models. Annals of Statistics 34:1733–1750.
   Web of Science ®Google Scholar
• Kackar, R. N., and D. A. Harville. 1981. Unbiasedness of two-stage estimation and prediction procedure for mixed linear models. Communications in Statistics – Theory and Methods 10:1249–1261.
   Web of Science ®Google Scholar
• Kackar, R. N., and D. A. Harville. 1984. Approximations for standard errors of estimators of fixed and random effect in mixed linear models. Journal of the American Statistical Association 79:853–862.
   Web of Science ®Google Scholar
• Marchetti, S., N. Tzavidis, and M. Pratesi. 2012. Non-parametric bootstrap mean squared error estimation for M-quantile estimators of small area averages, quantiles and poverty indicators. Computational Statistics and Data Analysis 56:2889–2902.
   Web of Science ®Google Scholar
• Mardia, K. V., and R. J. Marshall. 1984. Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika 71 (1):135–146.
   Web of Science ®Google Scholar
• Molina, I. 2009. Uncertainty under a multivariate nested-error regression model with logarithmic transformation. Journal of Multivariate Analysis 100:963–980.
   Web of Science ®Google Scholar
• Molina, I., and Y. Marhuenda. 2015. sae: An R package for small area estimation. The R Journal 7 (1):81–98.
   Google Scholar
• Prasad, N. G. N., and J. N. K. Rao. 1990. The estimation of mean squared error of small-area estimators. Journal of the American Statistical Association 85:163–171.
   Web of Science ®Google Scholar
• Rao, J. N. K., and I. Molina. 2015. Small area estimation. New York, NY: Wiley.
   Google Scholar
• Schafer, J. L., and R. M. Yucel. 2002. Computational strategies for multivariate linear mixed-effects models with missing values. Journal of Computational and Graphical Statistics 11:437–457.
   Web of Science ®Google Scholar
• Sweeting, T. J. 1980. Uniform asymptotic normality of the maximum likelihood estimator. The Annals of Statistics 8: 1375–1381.
   Web of Science ®Google Scholar
• Yucel, R. 2010. mlmmm: ML estimation under multivariate linear mixed models with missing values. R package version 0.3–1.2. Retrieved from http://CRAN.R-project.org/package=mlmmm.
   Google Scholar