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Regression analysis under link violation. (English) Zbl 0753.62041
A model $$y=g(\alpha+\beta x,\varepsilon)$$, $$\varepsilon\sim F(\varepsilon)$$, with an arbitrary function $$g$$ and an arbitrary distribution $$F$$ is considered. The problem is to estimate the vector $$\beta$$. It is shown that, under suitable assumptions on the criterion function, the vector $$\beta$$ is identifiable and that there exists an estimate of $$\beta$$. It appears that the maximum likelihood-type estimates are asymptotically robust against an incorrect choice of the function $$g$$. Also, it is shown the Wald and likelihood ratio tests for testing the hypothesis $$H: \beta W=0$$ are asymptotically robust in the above sense. At the end, a numerical example is presented.

##### MSC:
 62J99 Linear inference, regression 62F35 Robustness and adaptive procedures (parametric inference)
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