Small area estimation with spatially varying natural exponential families

References

• Pfeffermann D. New important developments in small area estimation. Stat Sci. 2013;28:40–68. doi: 10.1214/12-STS395
   Web of Science ®Google Scholar
• Rao JNK, Molina I. Small area estimation. 2nd ed. New Jersey: Wiley; 2015.
   Google Scholar
• Fay R, Herriot R. Estimators of income for small area places: an application of James–Stein procedures to census. J Am Stat Assoc. 1979;74:341–353. doi: 10.1080/01621459.1979.10482505
   Web of Science ®Google Scholar
• Ghosh M, Maiti T. Small-area estimation based on natural exponential family quadratic variance function models and survey weights. Biometrika. 2004;91:95–112. doi: 10.1093/biomet/91.1.95
   Web of Science ®Google Scholar
• Jiang J. Linear and generalized linear mixed models and their applications. New York: Springer; 2006.
   Google Scholar
• McCulloch CE, Searle SR. Generalized, linear, and mixed models. New York: Wiley; 2001.
   Google Scholar
• Bandyopadhyay D, Reich BJ, Slate EH. Bayesian modeling of multivariate spatial binary data with applications to dental caries. Stat Med. 2009;28:3492–3508. doi: 10.1002/sim.3647
   PubMed Web of Science ®Google Scholar
• Marhuenda Y, Molina I, Morales D. Small area estimation with spatio-temporal Fay–Herriot models. Comput Stat Data Anal. 2013;58:308–325. doi: 10.1016/j.csda.2012.09.002
   Web of Science ®Google Scholar
• Pratesi M, Salvati N. Small area estimation in the presence of correlated random area effects. J Off Stat. 2009;25:37–53.
   Web of Science ®Google Scholar
• Schmid T, Tzavidis N, Münnich R, Chambers R. Outlier robust small-area estimation under spatial correlation. Scand J Stat. 2016;43:806–826. doi: 10.1111/sjos.12205
   Web of Science ®Google Scholar
• Wakefield J. Disease mapping and spatial regression with count data. Biostatistics. 2007;8:158–183. doi: 10.1093/biostatistics/kxl008
   PubMed Web of Science ®Google Scholar
• Brunsdon C, Fotheringham AS, Charlton M. Geographically weighted regression: a method for exploring spatial non-stationarity. Geogr Anal. 1996;28:281–298. doi: 10.1111/j.1538-4632.1996.tb00936.x
   Web of Science ®Google Scholar
• Fotheringham AS, Brunsdon C, Charlton M. Geographically weighted regression. West Sussex: Wiley; 2002.
   Google Scholar
• Chambers R, Dreassi E, Salvati N. Disease mapping via negative binomial regression M-quantiles. Stat Med. 2014;33:4805–4824. doi: 10.1002/sim.6256
   PubMed Web of Science ®Google Scholar
• Chandra H, Salvati N, Chambers R, Tzavidis N. Small area estimation under spatial nonstationarity. Comput Stat Data Anal. 2012;56:2875–2888. doi: 10.1016/j.csda.2012.02.006
   Web of Science ®Google Scholar
• Chandra H, Salvati N, Chambers R. A spatially nonstationary Fay–Herriot model for small area estimation. J Surv Stat Methodol. 2015;3:109–135. doi: 10.1093/jssam/smu026
   Google Scholar
• Chandra H, Salvati N, Chambers R. Small area prediction of counts under a non-stationary spatial model. Spat Stat. 2017;20:30–56. doi: 10.1016/j.spasta.2017.01.004
   Web of Science ®Google Scholar
• Salvati N, Tzavidis N, Pratesi M, Chambers R. Small area estimation via m-quantile geographically weighted regression. Test. 2012;21:1–28. doi: 10.1007/s11749-010-0231-1
   Web of Science ®Google Scholar
• Tibshirani R, Hastie T. Local likelihood estimation. J Am Stat Assoc. 1987;82:559–567. doi: 10.1080/01621459.1987.10478466
   Web of Science ®Google Scholar
• Brent R. Algorithms for minimization without derivatives. Englewood Cliffs, NJ: Prentice-Hall; 1973.
   Google Scholar
• Prasad N, Rao JNK. The estimation of mean-squared errors of small-area estimators. J Am Stat Assoc. 1990;90:758–766.
   Google Scholar
• Datta GS, Rao JNK, Smith DD. On measuring the variability of small area estimators under a basic area level model. Biometrika. 2005;92:183–196. doi: 10.1093/biomet/92.1.183
   Web of Science ®Google Scholar
• Butar FB, Lahiri P. On measures of uncertainty of empirical Bayes small-area estimators. J Stat Plan Inference. 2003;112:63–76. doi: 10.1016/S0378-3758(02)00323-3
   Web of Science ®Google Scholar
• Hall P, Maiti T. On parametric bootstrap methods for small area prediction. J R Stat Soc: Ser B. 2006;68:221–238. doi: 10.1111/j.1467-9868.2006.00541.x
   Google Scholar
• Bell WR, Datta GS, Ghosh M. Benchmarking small area estimators. Biometrika. 2013;100:189–202. doi: 10.1093/biomet/ass063
   Web of Science ®Google Scholar
• Datta GS, Ghosh M, Steorts R, Maples J. Bayesian benchmarking with applications to small area estimation. Test. 2011;20:574–588. doi: 10.1007/s11749-010-0218-y
   Web of Science ®Google Scholar
• Steorts R, Ghosh M. On estimation of mean squared errors of benchmarked empirical Bayes estimators. Stat Sin. 2013;23:749–767.
   Web of Science ®Google Scholar
• Kubokawa T, Hasukawa M, Takahashi K. On measuring uncertainty of benchmarked predictors with application to disease risk estimate. Scand J Stat. 2014;35:394–413. doi: 10.1111/sjos.12040
   Google Scholar
• Clayton D, Kaldor J. Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics. 1987;43:671–681. doi: 10.2307/2532003
   PubMed Web of Science ®Google Scholar
• Silva AR, Rodrigues TCV. Geographically weighted negative binomial regression – incorporating overdispersion. Stat Comput. 2014;24:769–783.
   Web of Science ®Google Scholar
• Williams DA. The analysis of binary responses from toxicological experiments involving reproduction and teratogenicity. Biometrics. 1975;31:949–952. doi: 10.2307/2529820
   PubMed Web of Science ®Google Scholar
• Escaramis G, Carrasco JL, Ascaso C. Detection of significant disease risks using a spatial conditional autoregressive model. Biometrics. 2008;64:1043–1053. doi: 10.1111/j.1541-0420.2007.00981.x
   PubMed Web of Science ®Google Scholar
• Goicoa T, Ugarte MD, Etxeberria J, Militino AF. Comparing CAR and P-spline models in spatial disease mapping. Environ Ecol Stat. 2012;19:573–599. doi: 10.1007/s10651-012-0201-8
   Web of Science ®Google Scholar
• Ugarte MD, Adin A, Goicoa T. On fitting spatio-temporal disease mapping models using approximate Bayesian inference. Stat Methods Med Res. 2014;23:507–530. doi: 10.1177/0962280214527528
   PubMed Web of Science ®Google Scholar
• Rue H, Martino S, Chopin N. Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J R Stat Soc Ser B. 2009;71:319–392. doi: 10.1111/j.1467-9868.2008.00700.x
   Web of Science ®Google Scholar
• Molina I, Rao JNK. Small area estimation of poverty indicators. Can J Stat. 2010;38:369–385. doi: 10.1002/cjs.10051
   Web of Science ®Google Scholar