Inferential issues in model-based small area estimation: some  new development

J. N. K. Rao

doi:https://doi.org/10.59170/stattrans-2015-026

Inferential issues in model-based small area estimation: some new development

J. N. K. Rao Carleton University, Ottawa, Canada Statistics in Transition new series, vol. 16, 2015, 4, pages: 491-510 Published online: 1 December 2015 https://doi.org/10.59170/stattrans-2015-026

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ABSTRACT

Small area estimation (SAE) has seen a rapid growth over the past 10 years or so. Earlier work is covered in the author's book (Rao 2003). The main purpose of this paper is to highlight some new developments in model-based SAE since the publication of the author's book. A large part of the new theory addressed practical issues associated with the model-based approach, and we present some of those methods for area level and unit level models. We also briefly mention some new work on synthetic estimation of area means or totals based on implicit models.

KEYWORDS

area level models, complex parameters, informative sampling, model misspecification, robust estimation, unit level models.

REFERENCES

ARIMA, S., DATTA, G. S., LISEO, B., (2015). Accounting for measurement errors in SAE: an overview, in Analysis of Poverty Data by Small Area Methods, M. Pratesi (Ed.), Hoboken: Wiley (in press).

BATTESE, G. E., HARTER, R. M., FULLER, W. A., (1988). An error component model for prediction of county crop areas using survey and satellite data. Journal of the American Statistical Association, 83, 28-36.

BELL, W. R., DATTA, G. S., GHOSH, M., (2011). Benchmarking small area estimators. Biometrika, 100, 189-202.

BERG, E., CHANDRA, H., (2014). Small area prediction for a unit-level lognormal model. Computational Statistics and Data Analysis, 78, 158-175.

CASAS-CORDERO, C., ENCINA, J., LAHIRI, P.,(2015). Poverty mapping for the Chilean Comunas, in Analysis of Poverty data by Small Area Methods, M. Pratesi (Ed.), Hoboken: Wiley (in press).

CHAMBERS, R., CHANDRA, H., SALVATI, N., TZAVIDIS, N., (2014). Outlier robust small area estimation. Journal of the Royal Statistical Society, Ser. B, 76, 47-69.

CHAMBERS, R., TZAVIDIS, N., (2006). M-quantile models for small area estimation. Biometrika, 93, 255-268.

CHATTERJEE, S., LAHIRI, P., LI, H., (2008). Parametric bootstrap approximation to the distribution of EBLUP and related prediction intervals in linear mixed models. Annals of Statistics, 36, 1221-1245.

DATTA, G. S., (2009). Model-based approach to small area estimation, in Sample Surveys: Inference and Analysis, D. Pfeffermann and C. R. Rao (Eds.), Vol. 29B, Amsterdam: North-Holland, pp. 251-288.

DATTA, G. S., RAO, J. N. K., TORABI, M., (2010). Pseudo-empirical Bayes estimation of small area means under a nested error linear regression model with functional measurement errors. Journal of Statistical Planning and Inference, 140, 2952-2962.

DATTA, G. S., KUBOKAWA, T., MOLINA, I., RAO, J. N. K., (2011a). Estimation of mean squared error of model-based small area estimators. Test,20, 367-388.

DATTA, G. S., GHOSH, M., STEORTS, S., MAPLES, J. J., (2011b). Bayesian benchmarking with applications to small area estimation. Test, 20, 574-588.

DIALLO, M., RAO, J. N. K., (2014). Small area estimation of complex parameters under unit level models with skew-normal errors. Proceedings of the Survey Research Methods Section, American Statistical Association.

ERCIULESCU, A. L., FULLER, W. A.,(2014). Parametric bootstrap procedures for small area prediction variance. Proceedings of the Survey Research Methods Section, American Statistical Association.

FAY, R. E., HERRIOT, R. A., (1979). Estimation of income from small places: an application of James-Stein procedures to census data. Journal of the American Statistical Association, 74, 269-277.

GHOSH, M., SINHA, K.,(2007). Empirical Bayes estimation in finite population sampling under functional measurement error models. Scandinavian Journal of Statistics, 33, 591-608.

GHOSH, M., SINHA, K., KIM, D.,(2006). Empirical and Hierarchical Bayesian estimation in finite population sampling under structural measurement error models. Journal of Statistical Planning and Inference, 137, 2759-2773.

HALL, P., MAITI, T., (2006). Nonparametric estimation of mean-squared prediction error in nested error regression models. Annals of Statistics, 34, 1733-1750.

HAN, B., (2013). Conditional Akaike information criterion in the Fay-Herriot model. Statistical Methodology, 11, 53-67.

JIANG, J., LAHIRI, P., (2006). Mixed model prediction and small area estimation. Test, 15, 1-96.

JIANG, J., RAO, J. S., GU, I., NGUYEN, T., (2008). Fence Methods for Mixed Model Selection. Annals of Statistics, 36, 1669-1692.

JIANG, J., RAO, J. S., NGUYEN, T., (2011). Best predictive small area estimation. Journal of the American Statistical Association, 106, 732-745.

JIANG, J., NGUYEN, T., RAO, J. S., (2014). Observed best prediction via nested –error regression with potentially misspecified mean and variance. Survey Methodology (in press).

JIANGO, V. D., HAZIZA, D., DUCHESNE, P.,(2013). Controlling the bias of robust small-area estimation. Biometrika, 100, 843-858.

LI, H., LAHIRI, P., (2010). An adjusted maximum likelihood method for solving small area estimation problems. Journal of Multivariate Analysis, 101, 882-892.

LUERY, D. M., (2011). Small area income and poverty estimates program. Proceedings of 27th SCORUS Conference, Jurmala, Latvia, pp. 93-107.

MARCHETTI, S., GIUSTI, C., PRATESI, M., SALVATI, N., GIANNOTTI, F., PEDRESCHI, D., RINIZIVILLO, S., PAPPALARDO, L., GABRIELLI, L.,(2015). Small area model based estimation using big data sources. Journal of Official Statistics, to appear.

MOLINA, I., RAO, J. N. K., (2010). Small area estimation of poverty indicators. Canadian Journal of Statistics, 38, 369-385.

MOLINA, I., RAO, J. N. K., DATTA, G. S., (2014). Small area estimation under a Fay-Herriot model with preliminary testing for the presence of random effects. Survey Methodology (in press).

MULLER, S., SCEALY, J. L., WELSH, A. H., (2013). Model selection in linear mixed models. Statistical Science, 28, 135-167.

OPSOMER, J. D., CLAESKENS, G., RANDALL, M.G., KAUERMANN, G.,BREIDT, F. J.,(2008). Nonparametric small area estimation using penalized spline regression. Journal of the Royal Statistical Society, Ser. B, 70, 265-286.

PFEFFERMANN, D., (2013). New important developments in small area estimation. Statistical Science, 28, 40-68.

PFEFFERMANN, D., SVERCHKOV, M.,(2007). Small-area estimation under informative probability sampling of areas and within selected areas. Journal of the American Statistical Association, 102, 1427-1439.

PFEFFERMANN, D., CORREA, S., (2012). Empirical bootstrap bias correction and estimation of prediction mean squared error in small area estimation. Biometrika, 457-472.

PRATESI , M., (2015). Small area model-based estimators using big data sources. Journal of Official Statistics (in press).

RANDRIANASOLO, T., TILLE, Y.,(2013). Small area estimation by splitting the sampling weights. Electronic Journal of Statistics, 7, 1835-1855.

RAO, J. N.K., (2003). Small Area Estimation. Hoboken: Wiley.

RAO, J. N. K., (2005). Inferential issues in small area estimation: some new developments. Statistics in Transition, 7, 513-526.

RAO, J. N. K., (2008). Some methods for small area estimation. Rivista Internazionale di Scienze Sociali, 4, 387-406.

RAO, J. N. K., SINHA, S. K., DUMITRESCU, L., (2014). Robust small area estimation under semi-parametric mixed models. Canadian Journal of Statistics, 42, 126-141.

RIVEST, L-P., VANDAL, N. (2003). Mean squared error estimation for small areas when the small area variances are estimated. Proceedings of the International Conference on Recent Advances in Survey Sampling. Technical Report No. 386, Laboratory for Research in Statistics and Probability, Carleton University, Ottawa, Canada.

SCHIRM, A. L., ZASLAVSKY, A. M., (1997). Reweighting households to develop micro simulation estimates for states. Proceedings of the 1997 Section on Survey Research Methods, American Statistical Association, pp.306-311.

SCHOCH, T., (2012). Robust unit-level small area estimation: a fast algorithm for large data sets. Austrian Journal of Statistics, 41, 243-265.

SINHA, S. K., RAO, J. N. K., (2009). Robust small area estimation. Canadian Journal of Statistics, 37, 381-399.

STEORTS, R., GHOSH, M., (2013). On estimation of mean squared errors of benchmarked empirical Bayes estimators. Statistica Sinica, 23, 749-767.

STUKEL, D. M., RAO, J. N .K.,(1999). Small-area estimation under two-stage nested error regression models. Journal of Statistical Planning and Inference, 78, 131-147.

TORABI, M., DATTA, G. S., RAO, J. N. K., (2009). Empirical Bayes estimation of small area means under a nested error linear regression model with measurement errors in the covariates. Scandinavian Journal of Statistics, 36, 355-368.

TZAVIDIS, N., CHAMBERS, R., (2005). Bias adjusted small area estimation with M-quantile models. Statistics in Transition, 7, 707-713.

VAIDA, F., BLANCHARD, S., (2005). Conditional Akaike information for mixed effect models. Biometrika, 92, 351-370.

VERRET, F., RAO, J. N. K., HIDIROGLOU, M. A., (2014). Model-based small area estimation under informative sampling. Survey Methodology (in press).

WANG, J., FULLER, W. A., (2003). The mean squared error of small area predictors constructed with estimated sampling variances. Journal of the American Statistical Association, 98, 718-723.

WANG, J., FULLER, W. A., QU, Y., (2008). Small area estimation under a restriction. Survey Methodology, 34, 29-36.

YBARRA, L. M. R., LOHR, S., (2008). Small area estimation when auxiliary information is measured with error. Biometrika, 95, 919-931.

YOSHIMORI, M., LAHIRI, P., (2014). A new adjusted maximum likelihood method for the Fay-Herriot small area model. Journal of Multivariate Analysis, 124, 281-294.

YOU, Y., RAO, J. N. K., (2002). A pseudo-empirical best linear unbiased prediction approach to small area estimation under survey weights. Canadian Journal of Statistics, 30, 431-439.

YOU, Y., RAO, J. N. K., HIDIROGLOU, M. A., (2013). On the performance of self-benchmarked small area estimates under the Fay-Herriot area level model. Survey Methodology, 39, 217-229