Higher Order Asymptotics Unleashed: Software Design for Nonlinear Heteroscedastic Regression

One of the main criticisms against the use of higher order asymptotics is that the algebraic expressions involved are far too complex to be derived by hand in a reasonable amount of time. A further drawback is that the results are so closely tuned to the specific problem at hand that they almost always exclude the possibility of transferring available computer code to a different though similar problem. The aim of this article is to show that higher order asymptotics can be implemented in a general and flexible way so as to provide easy-to-use and self-contained software useful in routine data analysis. The programming strategy we develop easily applies to many parametric models. We illustrate it by describing the design of the core routines of the nlreg section of the S-Plus library HOA which implements higher order solutions for nonlinear heteroscedastic regression models.