Abstract
In this paper we investigate the prediction of the population total T = Σ N k=1 Y k under regression superpopulation models when the explanatory variable vector x is measured with error. Predictors T ̂ of the population total T which are functions of estimators \\ ̂ gb of the regression coefficient parameter β are investigated. In particular, by considering the ordinary least-squares estimator of β, we have the best unbiased predictor (BLU — Royall, 1976, Bolfarine and Zacks, 1992) of T, denoted by T ̂ BLU . Exploring the asymptotic normality of \\ ̂ gb under a set of assumptions, we study the asymptotic behavior of the predictor T ̂ , establishing its asymptotic normality. In the case of unique and several explanatory variables, comparisons are made in terms of the predictive variances of the asymptotic distributions. Surprisingly, the main conclusion is that T ̂ BLU is the predictor that behaves asymptotically best.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.