Tests for the choice of approximative models in nonlinear regression when the variance is unknown. (English) Zbl 0808.62059

Summary: Nonlinear regression models are used in many fields. Often the regression for observation-covariate pairs \((X(t_ i), t_ i)\) is modeled as \(X(t_ i)= f(t_ i)+ \varepsilon (t_ i)\), \(i=1,\dots, n\), where \(f\) is the continuous possible nonlinear mean function, while the \((\varepsilon (t_ i) )_{i=1,\dots, n}\) are zero mean, i.i.d. random errors having finite variance \(\sigma^ 2\). The least squares methods for estimation of \(f\) are usually based upon a given parametric form of \(f\).
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 \(\sigma^ 2\). The numerical results of a simulation study seem satisfactory.


62J02 General nonlinear regression
62F12 Asymptotic properties of parametric estimators
62F03 Parametric hypothesis testing
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