Inference after variable selection in linear regression models

Abstract

We explore the impact of variable selection on statistical inferences in linear regression models. In particular, the generalized final prediction error criterion of Shibata (1984) is considered and it is found, among other things, that inferences on the regression coefficients are impaired by the variable selection procedure. Most notably, the size of the nominal confidence sets tend to be inflated if they are derived based on the selected model. On the other hand, variable selection does not seem to have much impact on the inferences for the error variance. Our results complement those obtained by Pötscher (1991) in which testing procedures are used for variable selection.