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

The distribution of a linear predictor after model selection: Unconditional finite-sample distributions and asymptotic approximations