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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/208935We 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.Published at http://dx.doi.org/10.1214/074921706000000518 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)Statistics TheoryStatistical Finance62E15 (Primary) 62F10, 62F12, 62J05 (Secondary)The distribution of a linear predictor after model selection: Unconditional finite-sample distributions and asymptotic approximationstext