We propose two methods for benchmarking the observed best predictor (OBP; Jiang et al.[1]) in small area estimation under the Fay-Herriot model. Furthermore, we propose two methods for estimating the mean squared prediction error (MSPE) of the benchmarked OBP. Theoretical and empirical properties of the benchmarked OBP as well as its MSPE estimators are studied. A real-data example is considered.
JiangJ, NguyenT and RaoJS. Best Predictive Small Area Estimation. J Am Stat Assoc2011; 106: 732–745.
2.
JiangJ.Linear and Generalized Linear Mixed Models and Their Applications. New York: Springer, 2007.
3.
YouY. and RaoJNK. Pseudo Hierarchical Bayes Small Area Estimation Combining Unit Level Models and Survey Weights. J Stat Plan Inference2003; 111: 197–208.
4.
PfeffermannD and BarnardCH. Some new estimators for small-area means with application to the assessment of Farmland values. J Bus Econ Stat1997; 9: 73–84.
5.
IsakiCT, TsayJH and FullerWA. Estimation of census adjustment factors. Surv Methodol2000; 26: 31–42.
6.
YouY and RaoJNK. A pseudo-empirical best linear unbiased prediction approach to small area estimation using survey weights. Can J Stat2002; 30: 431–439.
7.
WangJ, FullerWA and QuY.Small area estimation under a restriction. Surv Methodol2008; 34: 29–36.
8.
FirthD and BennettKE. Robust models in probability sampling. J Roy Stat Soc B1998; 60: 3–21.
9.
ZhengH and LittleRJ. Penalized spline model-based estimation of the finite population total from probability-proportional-to-size samples. J Off Stat2003; 19: 99–117.
10.
ZhengH and LittleRJ. Inference for the population total from probability-proportional-to-size samples based on predictions from a penalized spline nonparametric model. J Off Stat2005: 21: 1–20.
11.
YouY, RaoJNK and HidiroglouM.On the performance of self benchmarked small area estimators under the Fay-Herriot area level model. Surv Methodol2013; 39: 217–229.
12.
PrasadNGN and RaoJNK. The estimation of mean squared errors of small area estimators. J Am Stat Assoc1990; 85: 163–171.
13.
LahiriP and RaoJNK. Robust estimation of mean squared error of small area estimators. J Am Stat Assoc1995; 90: 758–766.
14.
DattaGS and LahiriP.A unified measure of uncertainty of estimated best linear unbiased predictors in small area estimation problems. Stat Sin2000; 20: 613–627.
15.
JiangJ and LahiriP.Empirical best prediction for small area inference with binary data. Ann Inst Stat Math2001; 53: 217–243.
16.
DattaGS, RaoJNK and SmithDD.On measuring the variability of small area estimators under a basic area level model. Biometrika2005; 92: 183–196.
17.
JiangJ, LahiriP and WanS.A unified jackknife theory for empirical best prediction with M-estimation. Ann Stat2002; 30: 1782–1810.
18.
JiangJ, LahiriP and NguyenT.A unified Monte-Carlo jackknife for small area estimation after model selection. Ann Math Sci Appl2018; 3: 405–438.
19.
JiangJ, NguyenT and RaoJS. Fence method for nonparametric small area estimation. Surv Methodol2010; 36: 3–11.
20.
BandyopadhyayR.Benchmarking of Observed Best Predicror. PhD Thesis, University of California, Davis, USA, 2017.
21.
MorrisCN and ChristiansenCL. Hierarchical models for ranking and for identifying extremes with applications. In Bayes Statistics 5. Oxford: Oxford University Press, 1995.
22.
DattaGS, LahiriP and MaitiT. Empirical Bayes estimation of median income of four-person families by state using time series and cross-sectional data. J Stat Plan Inference2002; 102: 83–97.
23.
GaneshN.Simultaneous credible intervals for small area estimation problems. J Multivar Anal2009; 100: 1610–1621.
24.
HarvilleDA. Extension of the Gauss-Markov Theorem to include the estimation of random effects. Ann Stat1976; 4: 384–395.
25.
RobinsonGK. That BLUP Is a good thing: The estimation of random effects. Stat Sci1991; 6: 15–32.
