The density functions of R2 and [formula omitted], and their risk performance under asymmetric loss in misspecified linear regression models

Abstract

In this paper we derive the density functions of R 2 and the ‘adjusted’ R 2 (say, R 2 ), and examine their risk performance under asymmetric loss when there are two types of misspecification. One is exclusion of relevant variables and the other is inclusion of irrelevant variables. It is shown numerically that both R 2 and R 2 tend to underestimate when there are omitted variables, and both R 2 and R 2 tend to overestimate when there are irrelevant variables. The risk dominance of R 2 over R 2 depends on whether or not overestimation is more serious than underestimation.