Test for the choice of approximative models in nonlinear regression when the variance is unknown

Abstract

Nonlinear regression models are used in many fields. Often the regression for observation-covariate pairs (X(ti), ti) is modeled as X(ti) =f(ti) + [d](fi), i = 1,. .. , n, where f is the continuous possible nonlinear mean function, while the ([d](ti))i=1.....nare zero mean, i.i.d. random errors having finite variance [d]2. The least squares methods for estimation of f are usually based upon a given parametric form of f. In this article we develop two statistical tests, one for testing that f belongs to a given class of functions possibly discontinuous in their first derivative, and another one for comparing two such classes. This is done by introducing an appropriate estimate of the unknown variance [d]2. The numerical results of a simulation study seem satisfactory.