Cecilia Garcia-Peñalosa: cecilia.garcia-penalosa[at]univ-amu.fr
This work introduces a theoretical foundation for a procedure called `testing-based forward model selection' in regression problems. Forward selection is a general term refering to a model selection procedure which inductively selects covariates that add predictive power into a working statistical model. This paper considers the use of testing procedures, derived from traditional statistical hypothesis testing, as a criterion for deciding which variable to include next and when to stop including variables. Probabilistic bounds for prediction error and number of selected covariates are proved for the proposed procedure. The general result is illustrated by an example with heteroskedastic data where Huber-Eicker-White standard errors are used to construct tests. The performance of the testing-based forward selection is compared to Lasso and Post-Lasso in simulation studies. Finally, the use of testingbased forward selection is illustrated with an application to estimating the effects of institution quality on aggregate economic output.