Nonlinear regression: Third order significance

Abstract

Some recent methods of third order asymptotics produce remarkably accurate significance prob abilities but implicitly require the variable to have the same dimension as the parameter. A method for constructing an approximate ancillary given in Fraser & Reid (1995) extends these methods to general models with asymptotic properties. These extensions are used to give third order significance for a real parameter in a non-linear regression model. Emphasis is placed on the normal error model but extends to the non-normal additive error case and to generalized linear and nonlinear models; discussion here is restricted to the known variance case. Examples are given illustrating accuracy and generality, and comparisons are made with some first order methods.