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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.

##### MSC:
 62J02 General nonlinear regression 62F12 Asymptotic properties of parametric estimators 62F03 Parametric hypothesis testing
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##### References:
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