UC Santa Barbara

We consider an approach to prediction in linear model when values of the future explanatory variables are unavailable, we predict a future response y f at a future sample point x f when some components of x f are unavailable. We consider both the cases where x f are dependent and independent but normally distributed. A Taylor expansion is used to derive an approximation to the predictive density, and the influence of missing future explanatory variables (the loss or discrepancy) is assessed using the Kullback-Leibler measure of divergence. This discrepancy is compared in different scenarios including the situation where the missing variables are dropped entirely. © 2011 Copyright Taylor and Francis Group, LLC.