Asymptotics for EBLUPs: Nested Error Regression Models

References

• Arora, V., and Lahiri, P. (1997), “On the Superiority of the Bayesian Method Over the BLUP in Small Area Estimation Problems,” Statistica Sinica, 7, 1053–1063.
   Web of Science ®Google Scholar
• Battese, G. E., Harter, R. M., and Fuller, W. A. (1988), “An Error-components Model for Prediction of County Crop Areas Using Survey and Satellite Data,” Journal of the American Statistical Association, 83, 28–36. DOI: 10.1080/01621459.1988.10478561.
   Web of Science ®Google Scholar
• Chatterjee, S., Lahiri, P., and Li, H. (2008), “Parametric Bootstrap Approximation to the Distribution of Eblup and Related Prediction Intervals in Linear Mixed Models,” The Annals of Statistics, 36, 1221–1245. DOI: 10.1214/07-AOS512.
   Web of Science ®Google Scholar
• Das, K., Jiang, J., and Rao, J. N. K. (2004), “Mean Squared Error of Empirical Predictor,” The Annals of Statistics, 32, 818–840. DOI: 10.1214/009053604000000201.
   Web of Science ®Google Scholar
• Datta, G. S., and Lahiri, P. (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
• Gelman, A., and Hill, J. (2006), Data Analysis using Regression and Multilevel/Hierarchical Models, Cambridge, UK: Cambridge University Press.
   Google Scholar
• Henderson, C. R. (1975), “Best Linear Unbiased Estimation and Prediction Under a Selection Model,” Biometrics, 31, 423–447. DOI: 10.2307/2529430.
   PubMed Web of Science ®Google Scholar
• Henderson, C. R. (1984), Application of Linear Models in Animal Breeding, Guelph: University of Guelph Press.
   Google Scholar
• Henderson, C. R., Kempthorne, O., Searle, S. R., and Von Krosigk, C. (1959), “The Estimation of Environmental and Genetic Trends From Records Subject to Culling,” Biometrics, 15, 192–218. DOI: 10.2307/2527669.
   Web of Science ®Google Scholar
• Jiang, J. (1998), “Asymptotic Properties of the Empirical BLUP and BLUE in Mixed Linear Models,” Statistica Sinica, 8, 861–885.
   Web of Science ®Google Scholar
• Jiang, J., Lahiri, P., and Wan, S.-M. (2002), “A Unified Jackknife Theory for Empirical Best Prediction With M-estimation,” The Annals of Statistics, 30, 1782–1810. DOI: 10.1214/aos/1043351257.
   Web of Science ®Google Scholar
• Kackar, R. N., and Harville, D. A. (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.
   Web of Science ®Google Scholar
• Lange, N., and Ryan, L. (1989), “Assessing Normality in Random Effects Models,” The Annals of Statistics, 17, 624–642. DOI: 10.1214/aos/1176347130.
   Web of Science ®Google Scholar
• Lyu, Z., and Welsh, A. H. (2021), “Increasing Cluster Size Asymptotics for Nested Error Regression Models,” Available at https://arxiv.org/abs/2101.08951
   Google Scholar
• Nobre, J. S., and Singer, J. (2007), “Residual Analysis for Linear Mixed Models,” Biometrical Journal, 49, 863–875.
   PubMed Web of Science ®Google Scholar
• Pinheiro, J. C., and Bates, D. M. (2000), Mixed-Effects Models in S and S-Plus. New York: Springer.
   Google Scholar
• Prasad, N., and Rao, J. (1990), “The Estimation of the Mean Squared Error of Small-Area Estimators,” Journal of the American Statistical Association, 85, 163–171. DOI: 10.1080/01621459.1990.10475320.
   Web of Science ®Google Scholar
• Pratesi, M. (2016), Analysis of Poverty Data by Small Area Estimation. New York: Wiley.
   Google Scholar
• Robinson, G. K. (1991), “That BLUP is a Good Thing: The Estimation of Random Effects,” Statistical Science, 6, 15–32.
   Google Scholar
• Schützenmeister, A., Jensen, U., and Piepho, H. (2012), “Checking Normality and Homoscedasticity in the General Linear Model Using Diagnostic Plots,” Communications in Statistics – Simulation and Computation, 41, 141–154. DOI: 10.1080/03610918.2011.582560.
   Web of Science ®Google Scholar
• Searle, S. R., Casella, G., and McCulloch, C. E. (1992), Variance Components. New York: Wiley.
   Google Scholar
• Verbeke, G., and Molenberghs, G. (2000), Linear Mixed Models for Longitudinal Data. New York: Springer.
   Google Scholar
• Yoon, H.-J., and Welsh, A. H. (2020), “On the Effect of Ignoring Correlation in the Covariates When Fitting Linear Mixed Models,” Journal of Statistical Planning and Inference, 204, 18–34. DOI: 10.1016/j.jspi.2019.04.001.
   Web of Science ®Google Scholar