The kullback - leibler approximation of the marginal posterior density: An application to the linear functional model

The main purpose of this paper is to introduce the Kullback - Leibler approximation to investigate the estimation of the unobserved x values in a simple linear regression model when the variables are measured vith error. The mean and the variance of the Kullback- Leibler approximatin are shown to coincide with the estimators considered by Fuller, (1987, p.38). The Kulback-Leibler approximation in the modal approximation (Kass et al., 1990) of the exact marginal posterior of the real value x.