  We analyze the (unconditional) distribution of a linear predictor that is
constructed after a data-driven model selection step in a linear regression
model. First, we derive the exact finite-sample cumulative distribution
function (cdf) of the linear predictor, and a simple approximation to this
(complicated) cdf. We then analyze the large-sample limit behavior of these
cdfs, in the fixed-parameter case and under local alternatives.
