Invariance, Nonlinear Models, and Asymptotic Tests.

The invariance properties of several asymptotic tests are studied: invariance to hypothesis representation, reparameterization, and rescaling. Noninvariant tests include Wald tests, variants of LM tests, and Neyman's C(" alpha") tests. For all these tests, simply changing measurement units can lead to vastly different results, e.g. in models with Box-Cox transformations. Various consistent estimators of the information matrix produce tests with different invariance properties. Sufficient conditions are established under which a generalized C(" alpha") test becomes invariant to hypothesis reformulations, reparameterizations, and rescaling. In many practical cases, invariant C(" alpha") tests are much cheaper to compute than other invariant tests (e.g., LR tests). Copyright 1991 by The Econometric Society.