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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.

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