Testing goodness-of-fit for nonlinear regression models with heterogeneous variances. (English) Zbl 0900.62102
Summary: This paper describes a method for testing a parametric model for the regression function and for the variance function in a parametric nonlinear regression model. The procedure is based on the robustness properties of various estimators of the parameters, the test statistics being simply equal to the normalized differences between two different estimators. The estimation of the normalizing factor using the first-order approximations of the distribution of estimators is strongly dependent on the chosen model, and thus leads to low values of the power of the test. We propose to use wild bootstrap method to estimate this normalizing factor. This method is robust to a misspecification of the variance function. Moreover, the simulation study shows that the wild bootstrap method has nearly no effect on the probability that the test rejects the null hypothesis.
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