Mixed model prediction and small area estimation

Test

Volumn 15, Issue 1, 2006, Pages 1-96

  Jiang, Jiming ^a,c   Lahiri, P ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF MARYLAND   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Benchmarking; Borrowing strength; Design consistency; EBLUP; Empirical Bayes; Generalized linear mixed models; Higher order asymptotics; Mean squared errors; Resampling methods; Sample surveys; Variance components

Indexed keywords

EID: 33646692461     PISSN: 11330686     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02595419     Document Type: Article

References (166)

1. ARORA, V., LAHIRI, P., and MUKHERJEE, K. (1997). Empirical Bayes estimation of finite population means from complex surveys. Journal of the American Statistical Association, 92:1555-1562.
2. BARNDORFF-NIELSEN, O. (1983). On a formula for the distribution of the maximum likelihood estimator. Biometrika, 70:343-365.
3. BASU, R., GHOSH, J. K., and MUKERJEE, R. (2003). Empirical Bayes prediction intervals in a normal regression model: Higher order asymptotics. Statistics & Probability Letters, 63:197-203.
4. 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, 80:28-36.
5. BECKMAN, R. J., NACHTSHEIM, C. J., and COOK, R. D. (1987). Diagnostics for mixed-model analysis of variance. Technometrics, 29:413-426.
6. BELL, W. (2001). Discussion with "Jackknife in the Fay-Herriott model with an example". In Proceeding of the Seminar on Funding Opportunity in Survey Research, pp. 98-104.
7. BOOTH, J. G. and HOBERT, J. P. (1998). Standard errors of predictors in generalized linear mixed models. Journal of the American Statistical Association, 93:262-272.
8. BOOTH, J. G. and HOBERT, J. P. (1999). Maximum generalized linear mixed model likelihood with an automated Monte Carlo EM algorithm. Journal of the Royal Statistical Society. Series B, 61:265-285.
9. BRACKSTONE, G. J. (1987). Small area data: policy issues and technical challenges. In R. Platek, J. N. K. Rao, C. E. Sarndal, and M. P. Singh, eds., Small Area Statistics, pp. 3-20. John Wiley & Sons, New York.
10. BRESLOW, N. E. and CLAYTON, D. G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88:9-25.
11. BUTAR, F. B. (1997). Empirical Bayes Methods in Survey Sampling. PhD Thesis, Dept. of Mathematics and Statistics, University of Nebraska-Lincoln.
12. BUTAR, F. B. and LAHIRI, P. (2003). On measures of uncertainty of empirical Bayes small area estimators. Model selection, model diagnostics, empirical Bayes and hierarchical Bayes, Special Issue II (Lincoln, NE, 1999). Journal of Statistical Planning and Inference, 112(1-2):63-76.
13. CALVIN, J. A. and SEDRANSK, J. (1991). Bayesian and frequentist predictive inference for the patterns of care studies. Journal of the American Statistical Association, 86:36-48.
14. CARLIN, B. P. and GELFAND, A. (1990). Approaches for empirical Bayes confidence intervals. Journal of the American Statistical Association, 85:105-114.
15. CARLIN, B. P. and GELFAND, A. (1991). A sample reuse method for accurate parametric empirical Bayes confidence intervals. Journal of the Royal Statistical Society. Series B, 53:189-200.
16. CARLIN, B. P. and Louis, T. A. (1996). Bayes and Empirical Bayes Methods for Data Analysis. Chapman and Hall, London.
17. CARTER, G. M. and ROLPH, J. E. (1974). Empirical Bayes methods applied to estimating fire alarm probabilities. Journal of the American Statistical Association, 69:880-885.
18. CHATTERJEE, S. and LAHIRI, P. (2002). Parametric bootstrap confidence interval in small area estimation problems. Unpublished manuscript.
19. CHAUDHURI, A. (1994). Small domain statistics: a review. Statistica Neerlandica, 48:215-236.
20. CHEN, S. and LAHIRI, P. (2002). A weighted jackknife MSPE estimator in small area estimation. In Proceedings of the Survey Research Methods Section, pp. 473-477. American Statistical Association.
21. CHEN, S. and LAHIRI, P. (2003a). A comparison of different MSPE estimators of EBLUP for the Fay-Herriot model. In Proceedings of the Survey Research Methods Section, pp. 905-911. American Statistical Association.
22. CHEN, S. and LAHIRI, P. (2003b). Jackknifing the mean square prediction error of EBLUP for the Fay-Herriot model. Unpublished manuscript.
23. CHEN, S. and LAHIRI, P. (2005). On mean squared prediction error estimation in small area estimation problems. In Proceedings of the Survey Research Methods Section. American Statistical Association. To appear.
24. CHEN, S., LAHIRI, P., and RAO, J. N. K. (2005). On mean square prediction error estimation for a non-normal Fay-Herriot model. Unpublished manuscript.
25. CHRISTENSEN, R., PEARSON, L. M., and JOHNSON, W. (1992). Case-deletion diagnostics for mixed models. Technometrics, 34:38-45.
26. CHRISTIANSEN, C. L. and MORRIS, C. N. (1994). README document, June 7, 1994, a seven-page latex tutorial for PRIMM. Available through StatLib, stat@lib.stat.cmu.edu.
27. CHRISTIANSEN, C. L. and MORRIS, C. N. (1996). Hierarchical Poisson regression modeling. In D. Berry and D. Stangl, eds., Bayesian Biostatistics, pp. 467-501. Marcel Dekker, New York.
28. CHRISTIANSEN, C. L. and MORRIS, C. N. (1997). Hierarchical Poisson regression modeling. Journal of the American Statistical Association, 92:618-632.
29. CITRO, C. F., COHEN, M. L., KALTON, G., and WEST, K. K. (1997). Small-area estimates of school-age children in poverty: Interim report I-evaluation of 1998 county estimates for title I allocation. National Academy Press, Washington.
30. COX, D. R. (1975). Prediction intervals and empirical Bayes confidence intervals. In J. Gani, ed., Perspectives in Probability and Statistics (Papers in honor of M. S. Bartlett), pp. 47-55. National Academic Press, Washington.
31. 2)dt: Application to logistic normal models. Journal of the American Statistical Association, 85:464-469.
32. DAS, K., JIANG, J., and RAO, J. N. K. (2004). Mean squared error of empirical predictor. The Annals of Statistics, 32:818-840.
33. DATTA, G. S. and GHOSH, M. (1991). Bayesian prediction in linear models: applications to small area estimation. The Annals of Statistics, 19:1746-1770.
34. DATTA, G. S., GHOSH, M., SMITH, D. D., and LAHIRI, P. (2002). On an asymptotic theory of conditional and unconditional coverage probabilities of empirical Bayes confidence intervals. Scandinavian Journal of Statistics, 29:139-152.
35. 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.
36. DATTA, G. S. and LAHIRI, P. (2001). Discussions on a paper by Efron and Gous. In Model Selection, Vol. 38 of IMS Lecture Notes/Monograph.
37. DATTA, G. S., RAO, J. N. K., and SMITH, D. D. (2005). On measuring the variability of small area estimators under a basic area level model. Biometrika, 92:183-196.
38. DEMPSTER, A. P. and RYAN, L. M. (1985). Weighted normal plots. Journal of the American Statistical Association, 80:845-850.
39. DIGGLE, P. J., LIANG, K. Y., and ZEGER, S. L. (1996). Analysis of Longitudinal Data. Oxford University Press, Oxford.
40. EFRON, B. (1975). Biased versus unbiased estimation. Advances in Mathematics, 16:259-277.
41. EFRON, B. and MORRIS, C. N. (1972). Limiting the risk of Bayes and empirical Bayes estimators. Part II: the empirical Bayes case. Journal of the American Statistical Association, 67:130-139.
42. EFRON, B. and MORRIS, C. N. (1973). Stein's estimation rule and its competitors- an empirical Bayes approach. Journal of the American Statistical Association, 68:117-130.
43. EFRON, B. and MORRIS, C. N. (1975). Data analysis using Stein's estimator and its generalizations. Journal of the American Statistical Association, 70:311-319.
44. FABRIZI, E. and LAHIRI, P. (2004). A new approximation to the Bayes information criterion in finite population sampling. Unpublished manuscript.
45. FAY, R. E. and HERRIOT, R. A. (1979). Estimates of income for small places: an application of James-Stein procedures to census data. Journal of the American Statistical Association, 74:269-277.
46. FULLER, W. A. (1990). Prediction of true values for the measurement error model. Contemporary Mathematics, 112:41-57.
47. GELMAN, A., CARLIN, J. B., STERN, H. S., and RUBIN, D. B. (1995). Bayesian Data Analysis. Chapman and Hall, London.
48. GERSHUNSKAYA, J. B. and LAHIRI, P. (2005). Variance estimation for domains in the U.S. Current Employment Statistics Program. In Proceedings of the Survey Research Methods Section. American Statistical Association. To appear.
49. GHOSH, M. and LAHIRI, P. (1987). Robust empirical Bayes estimation of means from stratified samples. Journal of the American Statistical Association, 82:1153-1162.
50. GHOSH, M. and LAHIRI, P. (1992). A hierarchical Bayes approach to small area estimation with auxiliary information (with discussion). In Bayesian Analysis in Statistics and Econometrics, pp. 107-125. Springer-Verlag, Berlin.
51. GHOSH, M. and MEEDEN, G. (1986). Empirical Bayes estimation in finite population sampling. Journal of the American Statistical Association, 81:1058-1062.
52. GHOSH, M. and MEEDEN, G. (1997). Bayesian Methods for Finite Population Sampling. Chapman and Hall, London.
53. GHOSH, M., NATARAJAN, K., STROUD, T. W. F., and CARLIN, B. P. (1998). Generalized linear models for small-area estimation. Journal of the American Statistical Association, 93:273-282.
54. GHOSH, M. and RAO, J. N. K. (1994). Small area estimation: An appraisal (with discussion). Statistical Science, 9:55-93.
55. GLICKMAN, H. and PFEFFERMANN, D. (2004). Mean square error approximation in small area estimation by use of parametric and nonparametric bootstrap. In Proceedings of the Survey Research Methods Section. American Statistical Association. To appear.
56. GOLDSTEIN, H. (1986). Multilevel mixed linear model analysis using iterative generalised least squares. Biometrika, 73:43-56.
57. HARTLEY, H. O. and RAO, J. N. K. (1967). Maximum likelihood estimation for the mixed analysis of variance model. Biometrika, 54:93-108.
58. HARVILLE, D. A. (1974). Bayesian inference for variance components using only error contrasts. Biometrika, 61:383-385.
59. HARVILLE, D. A. (1977). Maximum likelihood approaches to variance components estimation and related problems. Journal of the American Statistical Association, 72:320-340.
60. HARVILLE, D. A. (1990). BLUP (best linear unbiased prediction) and beyond. In D. Gianola and K. Hammond, eds., Advances in Statistical Methods for Genetic Improvement of Livestock, pp. 239-276. Springer-Verlag, New York.
61. HARVILLE, D. A. (1991). Comment on Robinson: estimation of random effects. Statistical Science, 6:35-39.
62. HENDERSON, C. R. (1948). Estimation of general, specific and maternal combining abilities in crosses among inbred lines of swine. PhD Thesis, Iowa State University, Ames, Iowa.
63. HENDERSON, C. R. (1950). Estimation of genetic parameters (abstract). The Annals of Mathematical Statistics, 21:309-310.
64. HENDERSON, C. R. (1953). Estimation of variance and covariance components. Biometrics, 9:226-252.
65. HENDERSON, C. R. (1973). Sire evaluation and genetic trends. In Proceedings of the Animal Breeding and Genetics Symposium in Honor of Dr. Jay L. Lush, pp. 10-41. Amer. Soc. Animal Sci. - Amer. Dairy Sci. Assoc. - Poultry Sci. Assoc., Champaign, IL.
66. HENDERSON, C. R., KEMPTHORNE, O., SEARLE, S. R., and VON KROSIGK, C. N. (1959). Estimation of environmental and genetic trends from records subject to culling. Biometrics, 15:192-218.
67. HEYDE, C. C. (1994). A quasi-likelihood approach to the REML estimating equations. Statistics & Probability Letters, 21:381-384.
68. HEYDE, C. C. (1997). Quasi-Likelihood and Its Application. Springer-Verlag, New York.
69. HILL, J. R. (1990). A general framework for model-based statistics. Biometrika, 77:115-26.
70. HINDE, J. (1982). Compound Poisson regression models. In R. Gilchrist, ed., GLIM 82: Proceedings of the International Conference on Generalized Linear Models, pp. 109-121. Springer-Verlag, Berlin.
71. HINRICHS, P. E. (2003). Consumer expenditure estimation incorporating generalized variance functions in hierarchical Bayes models. PhD Thesis, University of Nebraska-Lincoln.
72. IRELAND, C. T. and KULLBACK, S. (1968). Contingency tables with given marginals. Biometrika, 55:179-188.
73. ISAKI, C. T. and FULLER, W. A. (1982). Survey design under the regression superpopulation model. Journal of the American Statistical Association, 77:89-96.
74. JESKE, D. R. and HARVILLE, D. A. (1988). Prediction-interval procedures and (fixed-effects) confidence-interval procedures for mixed linear models. Communications in Statistics. Theory and Methods, 17:1053-1087.
75. JIANG, J. (1996). REML estimation: Asymptotic behavior and related topics. The Annals of Statistics, 24:255-286.
76. JIANG, J. (1997a). A derivation of BLUP - best linear unbiased predictor. Statistics & Probability Letters, 32:321-324.
77. JIANG, J. (1997b). Wald consistency and the method of sieves in REML estimation. The Annals of Statistics, 25:1781-1803.
78. JIANG, J. (1998a). Asymptotic properties of the empirical BLUP and BLUE in mixed linear models. Statistica Sinica, 8:861-885.
79. JIANG, J. (1998b). Consistent estimators in generalized linear mixed models. Journal of the American Statistical Association, 93:720-729.
80. JIANG, J. (1999). Conditional inference about generalized linear mixed models. The Annals of Statistics, 27:1974-2007.
81. JIANG, J. (2000a). A matrix inequality and its statistical applications. Linear Algebra and its Applications, 307:131-144.
82. JIANG, J. (2000b). A nonlinear Gauss-Seidel algorithm for inference about GLMM. Computational Statistics, 15:229-241.
83. JIANG, J. (2001). Goodness-of-fit tests for mixed model diagnostics. The Annals of Statistics, 29:1137-1164.
84. JIANG, J. (2003). Empirical best prediction for small area inference based on generalized linear mixed models. Journal of Statistical Planning and Inference, 111:117-127.
85. JIANG, J. (2006a). Comment on Song, Fan and Kalbfleisch: Maximization by parts in likelihood inference. Journal of the American Statistical Association. In press.
86. JIANG, J. (2006b). Linear and generalized linear mixed models and their applications. Springer-Verlag, working monograph.
87. JIANG, J. (2006c). Partially observed information and inference about non-Gaussian mixed linear models. The Annals of Statistics. In press.
88. JIANG, J., JIA, H., and CHEN, H. (2001a). Maximum posterior estimation of random effects in generalized linear mixed models. Statistica Sinica, 11:97-120.
89. JIANG, J. and LAHIRI, P. (2001). Empirical best prediction for small area inference with binary data. Annals of the Institute of Statistical Mathematics, 53:217-243.
90. JIANG, J. and LAHIRI, P. (2006). Estimation of finite population domain means - a model assisted empirical best prediction approach. Journal of the American Statistical Association. In press.
91. JIANG, J., LAHIRI, P., and WAN, S. (2002). A unified jackknife theory for empirical best prediction with M-estimation. The Annals of Statistics, 30:1782-1810.
92. 2 goodness-of-fit test with estimated cell frequencies. Sankhyā. Series A, 63:260-276.
93. JIANG, J. and RAO, J. S. (2003). Consistent procedures for mixed linear model selection. Sankhyā. Series A, 65:23-42.
94. JIANG, J. and ZHANG, W. (2001). Robust estimation in generalized linear mixed models. Biometrika, 88:753-765.
95. JIANG, J. and ZHANG, W. (2002). Distribution-free prediction intervals in mixed linear models. Statistica Sinica, 12:537-553.
96. JUAN-ALBACEA, Z. V. (2004). Small area estimation of sub-national poverty incidence. In Proceedings of the ADB-GTZ-CEPA Regional Conference on Poverty Monitoring. Manila, Philippines.
97. KACKAR, R. N. and HARVILLE, D. A. (1981). Unbiasedness of two-stage estimation and prediction procedures for mixed linear models. Communications in Statistics. Theory and Methods, 10:1249-1261.
98. 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.
99. KHURI, A. I. and SAHAI, H. (1985). Variance components analysis: a selective literature survey. International Statistical Review, 53:279-300.
100. KLEFFE, J. and RAO, J. N. K. (1992). Estimation of mean square error of empirical best linear unbiased predictors under a random error variance linear model. Journal of Multivariate Analysis, 43:1-15.
101. KOTT, P. (1989). Robust small domain estimation using random effects modelling. Survey Methodology, 15:3-12.
102. KUK, A. Y. C. (1995). Asymptotically unbiased estimation in generalized linear models with random effects. Journal of the Royal Statistical Society. Series B, 57:395-407.
103. LAHIRI, P. (1995). A jaccknife measure of uncertainty of linear empirical Bayes estimators. Unpublished manuscript.
104. LAHIRI, P. (2001). Model Selection, Vol. 38 of IMS Lecture Notes-Monograph Series. Institute of Mathematical Statistics, Beachwood, Ohio.
105. LAHIRI, P. (2003a). On the impact of bootstrap in survey sampling and small area estimation. Statistical Science, 18:199-210.
106. LAHIRI, P. (2003b). A review of empirical best linear unbiased prediction for the Fay-Herriot small-area model. The Philippine Statistician, 52:1-15.
107. LAHIRI, P. and LI, H. (2005). A fresh look at baseball data analysis. Unpublished report.
108. LAHIRI, P. and MAITI, T. (2002). Empirical Bayes estimation of relative risks in disease mapping. Calcutta Statistical Association Bulletin, 53:211-212.
109. LAHIRI, P. and MEZA, J. L. (2002). Small-area estimation. In A. H. El-Shaarawi and W. W. Piegorsch, eds., Encyclopedia of Environmetric, Vol. 4, pp. 2010-2014. John Wiley & Sons, Chichester.
110. LAHIRI, P. and RAO, J. N. K. (1995). Robust estimation of mean squared error of small area estimators. Journal of the American Statistical Association, 90:758-766.
111. LAIRD, N. M. and LOUIS, T. A. (1987). Empirical Bayes confidence intervals based on bootstrap samples. Journal of the American Statistical Association, 82:739-757.
112. LANGE, N. and RYAN, L. (1989). Assessing normality in random effects models. The Annals of Statistics, 17:624-642.
113. LEE, Y. and NELDER, J. A. (1996). Hierarchical generalized linear models (with discussion). Journal of the Royal Statistical Society. Series B, 58:619-678.
114. LI, H. (2005). Comparison of different small area estimators for complex survey data. Unpublished manuscript.
115. LIANG, K. Y. and ZEGER, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73:13-22.
116. LIN, X. and BRESLOW, N. E. (1996). Bias correction in generalized linear mixed models with multiple components of dispersion. Journal of the American Statistical Association, 91:1007-1016.
117. MALEC, D., SEDRANSK, J., MORIARITY, C. L., and LECLERE, F. B. (1997). Small area inference for binary variables in the National Health Interview Survey. Journal of the American Statistical Association, 92:815-826.
118. MARKER, D. A. (1999). Organization of small area estimators using generalized regression framework. Journal of Official Statistics, 15:1-24.
119. MARSHALL, R. J. (1991). A review of methods for the statistical analysis of spatial patterns of disease. Journal of the Royal Statistical Society. Series A, 154:421-441.
120. MCCULLAGH, P. and NELDER, J. A. (1989). Generalized Linear Models. Chapman and Hall, London, 2nd ed.
121. MCCULLOCH, C. E. (1994). Maximum likelihood variance components estimation for binary data. Journal of the American Statistical Association, 89:330-335.
122. MCCULLOCH, C. E. (1997). Maximum likelihood algorithms for generalized linear mixed models. Journal of the American Statistical Association, 92:162-170.
123. MCGILCHRIST, C. A. (1994). Estimation in generalized mixed models. Journal of the Royal Statistical Society. Series B, 56:61-69.
124. MEZA, J. L. (2003). Empirical Bayes estimation smoothing of relative risks in disease mapping. Journal of Statistical Planning and Inference, 112:43-62.
125. MEZA, J. L., CHEN, S., and LAHIRI, P. (2003). Estimation of lifetime alcohol abuse for Nebraska counties. Unpublished manuscript.
126. MEZA, J. L. and LAHIRI, P. (2005). A note on the Cp statistic under the nested error regression model. Survey Methodology, 31:105-109.
127. MILLER, J. J. (1977). Asymptotic properties of maximum likelihood estimates in the mixed model of analysis of variance. The Annals of Statistics, 5:746-762.
128. MORRIS, C. N. (1983a). Parametric empirical Bayes confidence intervals. In Scientific Inference, Data Analysis and Robustness, Vol. 4, pp. 25-50. Academic Press, New York.
129. MORRIS, C. N. (1983b). Parametric empirical Bayes inference: theory and applications. Journal of the American Statistical Association, 78:47-59.
130. MUKHOPADHYAY, P. (1998). Small Area Estimation in Survey Sampling. Narosa Publishing House, New Delhi.
131. NANDRAM, B. (1999). An empirical Bayes prediction interval for the finite population mean of a small area. Statistica Sinica, 9:325-343.
132. NANDRAM, B. and SEDRANSK, J. (1993). Empirical Bayes estimation for the finite population mean on the current occasion. Journal of the American Statistical Association, 88:994-1000.
133. NATARAJAN, R. and MCCULLOCH, C. E. (1995). A note on the existence of the posterior distribution for a class of mixed models for binomial responses. Biometrika, 82:639-643.
134. National Research Council (2000). Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology. National Academic Press, Washington.
135. NEYMAN, J. and SCOTT, E. (1948). Consistent estimates based on partially consistent observations. Econometrika, 16:1-32.
136. PATTERSON, H. D. and THOMPSON, R. (1971). Recovery of interblock information when block sizes are unequal. Biometrika, 58:545-554.
137. PFEFFERMANN, D. (1984). On extensions of the Gauss-Markov theorem to the case of stochastic regression coefficient. Journal of the Royal Statistical Society. Series B, 46:139-148.
138. PFEFFERMANN, D. (2002). Small area estimation - new developments and directions. International Statistical Review, 70:125-143.
139. PFEFFERMANN, D. and TILLER, R. (2002). Bootstrap approximation to prediction MSE for state-space models with estimated parameters. Technical Report, U.S. Bureau of Labor Statistics.
140. PINHEIRO, J. C. and BATES, D. M. (2000). Mixed-Effects Models in S and S-Plus. Springer-Verlag, New York, 2nd ed.
141. PRASAD, N. G. N. and RAO, J. N. K. (1990). The estimation of mean squared errors of small area estimators. Journal of the American Statistical Association, 85:163-171.
142. PRASAD, N. G. N. and RAO, J. N. K. (1999). On robust small area estimation using a simple random effects model. Survey Methodology, 25:67-72.
143. PRENTICE, R. L. (1988). Correlated binary regression with covariates specific to each binary observation. Biometrics, 44:1033-1048.
144. RAO, C. R. (1972). Estimation of variance and covariance components in linear models. Journal of the American Statistical Association, 67:112-115.
145. RAO, J. N. K. (1986). Synthetic estimators, SPREE and the best model based predictors. In Proceedings of the Conference on Survey Methods in Agriculture, pp. 1-16. U.S. Dept. of Agricultur, Washington, D.C.
146. RAO, J. N. K. (1999). Some recent advances in model-based small area estimation. Survey Methodology, 25:175-186.
147. RAO, J. N. K. (2001). EB and EBLUP in small area estimation. In S. E. Ahmed and N. Reid, eds., Empirical Bayes and Likelihoodinference, Vol. 148 of Lecture Notes in Statistics, pp. 33-43. Springer-Verlag, New York.
148. RAO, J. N. K. (2003). Small Area Estimation. John Wiley & Sons, New York.
149. RICHARDSON, A.M. and WELSH, A. H. (1994). Asymptotic properties of restricted maximum likelihood (REML) estimates for hierarchical mixed linear models. Australian Journal of Statistics, 36:31-43.
150. RIVEST, L. P. and BELMONTE, E. (1999). The conditional mean square errors of small area estimators in survey sampling. Technical Report, Laval University.
151. ROBINSON, D. L. (1987). Estimation and use of variance components. Journal of the Royal Statistical Society. Series D. The Statistician, 36:3-14.
152. ROBINSON, G. K. (1991). That BLUP is a good thing: The estimation of random effects (with discussion). Statistical Science, 6:15-51.
153. SCHALL, R. (1991). Estimation in generalized linear models with random effects. Biometrika, 78:719-727.
154. SEARLE, S. R., CASELLA, G., and MCCULLOCH, C. E. (1992). Variance Components. John Wiley & Sons, New York.
155. SHAW, R. G. (1987). Maximum-likelihood approaches applied to quantitative genetics of natural populations. Evolution, 41:812-826.
156. SINGH, A. C., STUKEL, D. M., and PFEFFERMANN, D. (1998). Bayesian versus frequentist measures of error in small area estimation. Journal of the Royal Statistical Society. Series B, 60:377-396.
157. SONG, P. X.-K., FAN, Y., and KALBFLEISCH, J. D. (2005). Maximization by parts in likelihood inference (with discussion). Journal of the American Statistical Association, 100(472):1145-1158.
158. SPEED, T. P. (1997). Restricted maximum likelihood (REML). In S. Kotz, C. B. Read, and D. L. Banks, eds., Encyclopedia of Statistical Sciences, Vol. 1, pp. 472-481. John Wiley & Sons, New York.
159. SÄRNDAL, C. E. (1984). Design-consistent versus model-dependent estimators for small domainss. Journal of the American Statistical Association, 79:624-6315.
160. TABUNDA, A. M. L. and ABANILLA, J. R. Y. (1997). A look at EBLUP and other small area estimates of poverty incidence at the city/municipality level. In Proceedings of 10th SRTC Annual Conference, pp. 73-97. Statistical Research and Training Center, Quezon City, Philippines.
161. THOMPSON, J., W. A. (1962). The problem of negative estimates of variance components. Annals of Mathematical Statistics, 33:273-289.
162. VERBYLA, A. P. (1990). A conditional derivation of residual maximum likelihood. Australian Journal of Statistics, 32:227-230.
163. WOLFINGER, R. and O'CONNELL, M. (1993). Generalized linear mixed models: a pseudo-likelihood approach. Journal of Statistical Computation and Simulation, 48:233-vi243.
164. WOLTER, K. M. (1985). Introduction to Variance Estimation. Springer-Verlag, New York.
165. YOU, Y. and RAO, J. N. K. (2002). A pseudo-empirical best linear unbiased prediction approach to small area estimation using survey weights. Canadian Journal of Statistics, 30(3):431-439.
166. ZEGER, S. L. and KARIM, R. M. (1991). Generalized linear models with random effects: a Gibbs sampling approach. Journal of the American Statistical Association, 86:79-86.