Gauss-Newton, Milliken-Graybill, and Exact Misspecification Testing Using Artificial Regressions

The Gauss-Newton regression (GNR) is widely used to compute Lagrange multiplier statistics. A regression described by Milliken and Graybill yields an exact F test in a certain class of nonlinear models which are linear under the null. This paper shows that the Milliken- Graybill regression is a GNR. Hence one interpretation of Milliken- Graybill is that they identied a class of nonlinear models for which the GNR yields an exact test.Specification testing; Milliken-Graybill Theorem; Gauss- Newton regression