Small-Area Estimation Method with Covariates Subject to Measurement Error

• Activity Number: 623
• Type: Invited
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: ASA
• Author(s): Gauri Sankar Datta*+ and Brunero Liseo and Serena Arima
• Companies: University of Georgia & U.S. Bureau of the Census and University of La Sapienza and University of Rome, La Sapienza
• Keywords: Gibbs sampling ; Hierarchical Bayes ; Median income ; Multivariate ; Propriety of posterior ; Structural measurement error

Abstract

A model by Fay and Herriot has been extensively used in developing model based estimates of small area means. Explanatory variables in this model are assumed to be free from measurement error. Often, however, the explanatory variables are obtained from surveys, and hence are subject to measurement error. When explanatory variables in Fay-Herriot model are measured with error, the standard treatment of Fay-Herriot model is not appropriate. Ybarra and Lohr (2008) considered a Fay-Herriot model in the small area context where explanatory variables are subject to functional measurement error. In this talk, we consider a multivariate Fay-Herriot model with structural measurement error to covariates. We pursue hierarchical Bayesian approach to this model based on suitable noninformative priors. Propriety of the resulting posteriors has been investigated. Illustration to estimation of four-person family median for the fifty U.S. States based on the Current Population Survey and other administrative data has been considered.