Projection-based methods of inference on subsets of parameters are useful for obtaining tests that do not over-reject the true parameter values. However, they are also often criticized for being conservative. We show that the usual method of projection can be modified to obtain tests that are as...

Projection-based tests for subsets of parameters are useful because they do not over-reject the true parameter values when either it is difficult to estimate the nuisance parameters or their identification status is questionable. However, they are also often criticized for being overly...

In this paper we introduce a new method of projection-type inference and describe it in the context of two stage least squares–based split-sample inference on subsets of structural coefficients in a linear instrumental variables regression model. The use of the new method not only guards...

In this paper we design two split-sample score tests for subsets of structural coefficients in a linear Instrumental Variables (IV) regression. Sample splitting serves two purposes - 1) validity of the resultant tests does not depend on the identifiability of the coefficients being tested and 2)...