Optimal significance levels of prior tests in the presence of multicollinearity

Abstract

A common approach in estimation is to use the same data to select a model by prior testing as well as to estimate the parameters in the final selection. A problem which arises is that the quadratic risk of such an estimator depends on the significance level of the prior test. The traditional 5 percent level can lead to unacceptably large quadratic risk particularly if the data exhibits high multicollinearity. Two criteria are considered for limiting the quadratic risk. It is shown that these criteria lead to easily calculated and quite accurate rules for determining the critical value of the prior test.

Keywords:

• prior test
• significance level
• critical value
• multicollinearity
• non-orthogonal
• quadratic risk
• regret function