Pseudo-empirical Bayes estimation of small area means under a nested error linear regression model with functional measurement errors

• Published in: Journal of statistical planning and inference Vol. 140; no. 11; pp. 2952 - 2962
• Main Authors: Datta, Gauri S., Rao, J.N.K., Torabi, Mahmoud
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 01.11.2010; Elsevier
• Subjects: Applications; Asymptotic optimality; Bayes risk; Decision theory; Exact sciences and technology; General topics; Insurance, economics, finance; Jackknife; Linear inference, regression; Mathematics; Mean squared prediction error; Measurement error; Probability and statistics; Pseudo-empirical Bayes predictor; Sciences and techniques of general use; Statistics; Mean squared prediction error; Asymptotic optimality; Bayes risk; Jackknife; Pseudo-empirical Bayes predictor; Measurement error; Error estimation; Prediction theory; Covariate; Stochastic process; Economic sciences; Statistical simulation; Linear model; Empirical Bayes estimation; Nested model; Bootstrap; Jackknife method; Bayes decision; Linear functional; Bayes estimation; Linear regression; Prediction; Statistical estimation; Statistical decision; Mean estimation; Statistical method; Statistical regression; Regression model; Decision theory; Filtering theory; Mean error; Econometrics; Resampling method
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2010.03.046

Small area estimation is studied under a nested error linear regression model with area level covariate subject to measurement error. Ghosh and Sinha (2007) obtained a pseudo-Bayes (PB) predictor of a small area mean and a corresponding pseudo-empirical Bayes (PEB) predictor, using the sample means of the observed covariate values to estimate the true covariate values. In this paper, we first derive an efficient PB predictor by using all the available data to estimate true covariate values. We then obtain a corresponding PEB predictor and show that it is asymptotically “optimal”. In addition, we employ a jackknife method to estimate the mean squared prediction error (MSPE) of the PEB predictor. Finally, we report the results of a simulation study on the performance of our PEB predictor and associated jackknife MSPE estimator. Our results show that the proposed PEB predictor can lead to significant gain in efficiency over the previously proposed PEB predictor. Area level models are also studied.