This paper uses dimension asymptotics to study why overfit linear regression models shouldbe compared out-of-sample; we let the number of predictors used by the larger model increasewith the number of observations so that their ratio remains uniformly positive. Under this limittheory, the naive...

This paper derives the asymptotic distribution of the F-test for the significance oflinear regression coefficients as both the number of regressors, k, and the number ofobservations, n, increase together so that their ratio remains positive in the limit. Theconventional critical values for this...