Department of Community Health Sciences, University of Manitoba, 750 Bannatyne Avenue, Winnipeg, Manitoba, Canada R3E 0W3. e-mail: email@example.com
SMALL AREA ESTIMATION USING SURVEY WEIGHTS WITH FUNCTIONAL MEASUREMENT ERROR IN THE COVARIATE
Article first published online: 28 SEP 2011
© 2011 Australian Statistical Publishing Association Inc.
Australian & New Zealand Journal of Statistics
Volume 53, Issue 2, pages 141–155, June 2011
How to Cite
Torabi, M. (2011), SMALL AREA ESTIMATION USING SURVEY WEIGHTS WITH FUNCTIONAL MEASUREMENT ERROR IN THE COVARIATE. Australian & New Zealand Journal of Statistics, 53: 141–155. doi: 10.1111/j.1467-842X.2011.00623.x
- Issue published online: 20 OCT 2011
- Article first published online: 28 SEP 2011
- Bayes risk;
- design consistency;
- mean squared prediction error;
- nested error regression model;
- pseudo-empirical Bayes predictor
Nested error linear regression models using survey weights have been studied in small area estimation to obtain efficient model-based and design-consistent estimators of small area means. The covariates in these nested error linear regression models are not subject to measurement errors. In practical applications, however, there are many situations in which the covariates are subject to measurement errors. In this paper, we develop a nested error linear regression model with an area-level covariate subject to functional measurement error. In particular, we propose a pseudo-empirical Bayes (PEB) predictor to estimate small area means. This predictor borrows strength across areas through the model and makes use of the survey weights to preserve the design consistency as the area sample size increases. We also 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.