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 powerful as the conventional tests for subsets of parameters. Like the usual projection-based methods, one can always put an upper bound to the rate at which the new method over-rejects the true value of the parameters of interest. The new method is described in the context of GMM with possibly weakly identified parameters
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