Improved power of one-sided tests

For the classical least-squares model it is often the case that shape or order restrictions are appropriate for the regression function, in the form of a set of linear inequality constraints imposed on the parameters. It is generally understood that the hypothesis test using the constrained alternative will provide higher power than the corresponding test using the unconstrained alternative. We present a formal proof that this is the case. Code for constrained estimation and testing is posted at www.stat.colostate.edu/~meyer/constrparam.htm.