Prediction of Finite Population Total in Measurement Error Models

Measurement error regression models are different from classical regression models mainly that the covariates are measured with errors. This paper deals with the prediction of finite population total based on regression models with measurement errors. General treatment of regression problems with measurement errors is considered in the pioneering book by Fuller (1987) and Cheng and Van Ness (1999). Later Sprent (1966) proposed methods based on generalized least-squares approach for estimating the regression coefficients. Lindley (1966) and Lindley and Sayad (1968) pioneered Bayesian approach to the problem. Further, contribution in Bayesian approach have been made by Zellner (1971) and Reilly and Patino-Leal (1981). Fuller (1975) points out not much research is done for problems in finite population with measurement error models. However, Bolfarine (1991) investigated the problem of predictors for finite population with errors in variable models. Recently, Kim and Saleh (2002, 2003, 2005) pioneered the application of preliminary test and shrinkage estimation methodology in measurement error models. Recent book of Saleh (2006) presents an overview on the theory of preliminary test and Shrinkage estimators. This paper contains the application of these ideas for the prediction of finite population totals using simple linear model with measurement errors.