Small Area Estimation: its Evolution in Five Decades

• Autorzy: Malay Ghosh
• Języki publikacji: EN

Abstrakty

EN

The paper is an attempt to trace some of the early developments of small area estimation. The basic papers such as the ones by Fay and Herriott (1979) and Battese, Harter and Fuller (1988) and their follow-ups are discussed in some details. Some of the current topics are also discussed. (original abstract)

Słowa kluczowe

EN

Small area estimates; Literature review; Development of science

PL

Statystyka małych obszarów; Przegląd literatury; Rozwój nauki

• Czasopismo: Statistics in Transition
• Rocznik: 2020
• Tom: 21
• Numer: nr 4 Special Issue
• Strony: 1--22

Twórcy

autor

Malay Ghosh

• University of Florida, USA

Bibliografia

• ARMAGAN, A., CLYDE, M., and DUNSON, D. B., (2013). Generalized double pareto shrinkage. Statistica Sinica, 23, pp. 119-143.
• ARMAGAN, A., DUNSON, D. B., LEE, J., and BAJWA, W. U., (2013). Posterior consistency in linear models under shrinkage priors. Biometrika, 100, pp. 1011-1018.
• BATTESE, G. E., HARTER, R. M., and FULLER, W. A., (1988). An error components model for prediction of county crop area using survey and satellite data. Journal of the American Statistical Association, 83, pp. 28-36.
• BELL, W. R., DATTA, G, S., and GHOSH, M., (2013). Benchmarking small area estimators. Biometrika, 100, pp. 189-202.
• BELL, W. R., BASEL, W. W., and MAPLES, J. J., (2016). An overview of U.S. Census Bureau's Small Area Income and Poverty Estimation Program. In Analysis of Poverty Data by Small Area Estimation. Ed. M. Pratesi. Wiley, UK, pp. 349-378.
• BERG, E., CECERE, W., and GHOSH, M., (2014). Small area estimation of county level farmland cash rental rates. Journal of Survey Statistics and Methodology, 2, pp. 1-37. Bivariate hierarchical Bayesian model for estimating cropland cash rental rates at the county level. Survey Methodology, in press.
• BOOTH, J. G., HOBERT, J., (1998). Standard errors of prediction in generalized linear mixed models. Journal of the American Statistical Association, 93, pp. 262-272.
• BUTAR, F. B., LAHIRI, P., (2003). On measures of uncertainty of empirical Bayes small area estimators. Journal of Statistical Planning and Inference, 112, pp. 63-76.
• CARVALHO, C. M., POLSON, N. G., SCOTT, J. G., (2010). The horseshoe estimator for sparse signals. Biometrika, 97, pp. 465-480.
• CHEN, S., LAHIRI, P., (2003).A comparison of different MPSE estimators of EBLUP for the Fay-Herriott model. In Proceedings of the Section on Survey Research Methods. Washington, D.C. American Statistical Association, pp. 903-911.
• DAS, K., JIANG, J., RAO, J. N. K., ((2004). Mean squared error of empirical predictor. Annals of Statistics, 32, pp. 818-840.
• DATTA, G. S., GHOSH, M., (1991). Bayesian prediction in linear models: applications to small area estimation. The Annals of Statistics, 19, pp. 1748-1770.
• DATTA, G., GHOSH, M., NANGIA, N., and NATARAJAN, K., (1996). Estimation of median income of four-person families: a Bayesian approach. In Bayesian Statistics and Econometrics: Essays in Honor of Arnold Zellner. Eds. D. Berry, K. Chaloner and J. Geweke. North Holland, pp. 129-140.
• DATTA, G. S., LAHIRI. P., (2000). A unified measure of uncertainty of estimated best linear unbiased predictors in small area estimation problems. Statistica Sinica, 10, pp. 613-627.
• 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, pp. 183-196.
• DATTA, G. S., GHOSH, M., STEORTS, R., and MAPLES, J. J., (2011). Bayesian benchmarking with applications to small area estimation. TEST, 20, pp. 574-588.
• DATTA, G. S., HALL, P., and MANDAL, A., (2011). Model selection and testing for the presence of small area effects and application to area level data. Journal of the American Statistical Association, 106, pp. 362-374.
• DATTA, G. S., MANDAL, A., (2015). Small area estimation with uncertain random effects. Journal of the American Statistical Association, 110, pp. 1735-1744.
• ELBERS, C., LANJOUW, J. O., and LANJOUW, P., (2003). Micro-level estimation of poverty and inequality. Econometrica, 71. pp. 355-364.
• ERCIULESCU, A. L., FRANCO, C., and LAHIRI, P., (2020). Use of administrative records in small area estimation. To appear in Administrative Records for Survey Methodology. Eds. P. Chun and M. Larson. Wiley, New York.
• FAY, R. E., (1987). Application of multivariate regression to small domain estimation. In Small Area Statistics. Eds. R. Platek, J.N.K. Rao, C-E Sarndal and M.P. Singh. Wiley New York, pp. 91-102.
• FAY, R. E., HERRIOT, R. A., (1979). Estimates of income for small places: an application of James-Stein procedure to census data. Journal of the American Statistical Association, 74, pp. 269-277.
• GHOSH, M., (1992). Constrained Bayes estimation with applications. Journal of the American Statistical Association, 87, pp. 533-540.
• GHOSH, M., RAO, J. N. K., (1994). Small area estimation: an appraisal. Statistical Science, pp. 55-93.
• GHOSH, M., NATARAJAN, K., STROUD, T. M. F., and CARLIN, B. P., (1998). Generalized linear models for small area estimation. Journal of the American Statistical Association, 93, pp. 273-282.
• GHOSH, M., STEORTS, R., (2013). Two-stage Bayesian benchmarking as applied to small area estimation. TEST, 22, pp. 670-687.
• GHOSH, M., KUBOKAWA, T., and KAWAKUBO, Y., (2015). Benchmarked empirical Bayes methods in multiplicative area-level models with risk evaluation. Biomerika, 102, pp. 647-659.
• GHOSH, M., MYUNG, J., and MOURA, F. A. S., (2018). Robust Bayesian small area estimation. Survey Methodology, 44, pp. 101-115.
• GONZALEZ, M. E., HOZA, C., (1978). Small area estimation with application to unemployment and housing estimates. Journal of the American Statistical Association, 73, pp. 7-15.
• GRIFFIN, J. E., BROWN, P. J., (2010). Inference with normal-gamma prior distributions in regression problems. Bayesian Analysis, 5, pp. 171-188.
• HANSEN, M. H., HURWITZ, W. N., and MADOW, W. G., (1953). Sample Survey Methods and Theory. Wiley, New York.
• HOLT, D., SMITH, T. M. F., and TOMBERLIN, T. J., (1979). A model-based approach for small subgroups of a population. Journal of the American Statistical Association, 74, pp. 405-410.
• JIANG, J., LAHIRI, P., (2001). Empirical best prediction of small area inference with binary data. Annals of the Institute of Statistical Mathematics, 53, pp. 217-243.
• JIANG, J., LAHIRI, P., and WAN, S-M., (2002). A unified jackknife theory. The Annals of Statistics, 30, pp. 1782-1810.
• JIANG, J., LAHIRI, P., (2006). Mixed model prediction and small area estimation (with discussion). TEST, 15, pp. 1-96.
• JIANG, J., NGUYEN, T., and RAO, J. S., (2011). Best predictive small area estimation. Journal of the American Statistical Association, 106, pp. 732-745.
• KACKAR, R. N., 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, pp. 853-862.
• LAHIRI, P., RAO, J. N. K., (1995). Robust estimation of mean squared error of small area estimators. Journal of the American Statistical Association, 90, pp. 758-766.
• LAHIRI, P., PRAMANIK, S., (2019). Evaluation of synthetic small area estimators using design-based methods. Austrian Journal of Statistics, 48, pp. 43-57.
• LOUIS, T. A., (1984). Estimating a population of parameter values using Bayes and empirical Bayes methods. Journal of the American Statistical Association, 79, pp. 393-398.
• MALEC, D., DAVIS, W. W., and CAO, X., (1999). Model-based small area estimates of overweight prevalence using sample selection adjustment. Statistics and Medicine, 18, pp. 3189-3200.
• MOLINA, I., RAO, J. N. K., (2010). Small area estimation of poverty indicators. Canadian Journal of Statistics, 38, pp. 369-385.
• MOLINA, I., RAO, J. N. K., and DATTA, G. S., (2015). Small area estimation under a Fay-Herriot model with preliminary testing for the presence of random effects. Survey Methodology.
• PFEFFERMANN, D., TILLER, R. B., (2005). Bootstrap approximation of prediction MSE for state-space models with estimated parameters. Journal of Time Series Analysis, 26, pp. 893-916.
• MORRIS, C. N., (1983). Parametric empirical Bayes inference: theory and applications. Journal of the American Statistical Association, 78, pp. 47-55.
• POLSON, N. G., SCOTT, J. G., (2010). Shrink globally, act locally: Sparse Bayesian regularization and prediction. Bayesian Statistics, 9, pp. 501-538.
• PFEFFERMANN, D., (2002). Small area estimation: new developments and direction. International Statistical Review, 70, pp. 125-143.
• PFEFFERMANN, D., (2013). New important developments in small area estimation. Statistical Science, 28, pp. 40-68.
• PRASAD, N. G. N., RAO, J. N. K., (1990). The estimation of mean squared error of small area estimators. Journal of the American Statistical Association, 85, pp. 163-171.
• RAGHUNATHAN, T. E., (1993). A quasi-empirical Bayes method for small area estimation. Journal of the American Statistical Association, 88, pp. 1444-1448.
• RAO, J. N. K., (2003). Some new developments in small area estimation. Journal of the Iranian Statistical Society, 2, pp. 145-169.
• RAO, J. N. K., (2006). Inferential issues in small area estimation: some new developments. Statistics in Transition, 7, pp. 523-526.
• RAO, J. N. K., Molina, I., (2015). Small Area Estimation, 2nd Edition. Wiley, New Jersey.
• SCOTT, J. G., BERGER, J. O., (2010). Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem. The Annals of Statistics, 38, pp. 2587-2619.
• SLUD, E. V., MAITI, T., (2006). Mean squared error estimation in transformed FayHerriot models. Journal of the Royal Statistical Society, B, 68, pp. 239-257.
• TANG, X., GHOSH, M., Ha, N-S., and SEDRANSK, J., (2018). Modeling random effects using global-local shrinkage priors in small area estimation. Journal of the American Statistical Association, 113, pp. 1476-1489.
• WANG, J., FULLER, W. A., and QU, Y., (2008). Small area estimation under restriction. Survey Methodology, 34, pp. 29-36.
• YOSHIMORI, M., LAHIRI, P., (2014). A new adjusted maximum likelihood method for the Fay-Herriott small area model. Journal of Multivariate Analysis, 124, pp. 281-294.
• YOU, Y., RAO, J. N. K., and HIDIROGLOU, M. A., (2013). On the performance of self-benchmarked small area estimators under the Fay-Herriott area level model. Survey Methodology, 39, pp. 217-229.

Identyfikatory

DOI

10.21307/stattrans-2020-022