Empirical Bayes Estimation of Small Area Means under a Nested Error Linear Regression Model with Measurement Errors in the Covariates

• Published in: Scandinavian journal of statistics Vol. 36; no. 2; pp. 355 - 369
• Main Authors: TORABI, MAHMOUD, DATTA, GAURI S., RAO, J. N. K.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.06.2009; Blackwell Publishing; Blackwell; Danish Society for Theoretical Statistics
• Series: Scandinavian Journal of Statistics
• Subjects: Bayes estimators; Bayes risk; Bayesian analysis; Consistent estimators; Decision theory; empirical Bayes; Estimating techniques; Estimation methods; Estimators; Exact sciences and technology; General topics; jackknife method; Linear inference, regression; Linear regression; Mathematics; mean squared prediction error; Modeling; nested error model; Parametric inference; Probability and statistics; Regression analysis; Sample size; Sciences and techniques of general use; Statistical methods; Statistical variance; Statistics; Studies; Test data; nested error model; Error estimation; Variance estimation; empirical Bayes; Asymptotic optimality; Prediction theory; Covariate; Stochastic process; Economic sciences; Statistical simulation; Linear model; Variance; Empirical Bayes estimation; Nested model; Bayes risk; mean squared prediction error; Bootstrap; Jackknife method; Bayes decision; Measurement error; Bayes estimation; Estimation error; Covariance analysis; Linear regression; Prediction; Statistical estimation; Statistical decision; Variance analysis; Mean estimation; Empirical model; Statistical method; Statistical regression; Regression model; Decision theory; Filtering theory; Mean error; Econometrics; Application; Variance component; Resampling method
• ISSN: 0303-6898; 1467-9469
• DOI: 10.1111/j.1467-9469.2008.00623.x

Previously, small area estimation under a nested error linear regression model was studied with area level covariates subject to measurement error. However, the information on observed covariates was not used in finding the Bayes predictor of a small area mean. In this paper, we first derive the fully efficient Bayes predictor by utilizing all the available data. We then estimate the regression and variance component parameters in the model to get an empirical Bayes predictor and show that the EB predictor is asymptotically optimal. In addition, we employ the jackknife method to obtain an estimator of mean squared prediction error (MSPE) of the EB predictor. Finally, we report the results of a simulation study on the performance of our EB predictor and associated jackknife MSPE estimators. Our results show that the proposed EB predictor can lead to significant gain in efficiency over the previously proposed EB predictor.