Model Selection in High-Dimensional Linear Regression using Boosting with Multiple Testing

This paper studies model selection in high dimensional regression settings. We propose a Boosting with Multiple Testing (BMT) approach designed to address proxy signal contamination in environments with strongly correlated regressors, including settings driven by latent common factors. At each stage, at most one regressor is selected conditional on those already included, using a multiple testing threshold for the remaining candidates. Under stated dependence, detectability and design conditions, BMT recovers the exact true model with probability approaching one. A separate extension permits growing signal counts under additional restrictions. For fixed numbers of signals and proxies, we also establish recovery of an approximating model containing all true signals and no noise variables under a separate set of conditions. Following exact selection, fixed dimensional least squares has the oracle asymptotic distribution under the stated moment conditions. A theoretical comparison identifies designs and tuning sequences for which BMT is consistent while the Lasso is not. In the main Monte Carlo comparison, BMT has the highest median Matthews correlation coefficient and exact recovery rate and the lowest median coefficient root mean squared error among the compared specifications. Applications to U.S. emissions and inflation show that BMT combines sparse specifications with favourable forecast performance, including the lowest emissions forecasting errors in the reported comparisons and the best one quarter ahead forecasts in the baseline inflation comparison.