Joint inference based on Stein-type averaging estimators in the linear regression model

While averaging unrestricted with restricted estimators is known to reduce estimation risk, it is an open question whether this reduction in turn can improve inference. To analyze this question, we construct joint confidence regions centered at James–Stein averaging estimators in both homoskedastic and heteroskedastic linear regression models. These regions are asymptotically valid when the number of restrictions increases possibly proportionally with the sample size. When used for hypothesis testing, we show that suitable restrictions enhance power over the standard
F-test. We study the practical implementation through simulations and an application to consumption-based asset pricing.