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Robust regression with both continuous and categorical predictors. (English) Zbl 0954.62030

Summary: We deal with robust estimation in linear models of the form: \[ y_i=x_{1i}' \beta_1+ x_{2i}' \beta_2+ e_i\quad (i=1, \dots,n), \] in which the \(x_{1i}\) are fixed 0-1 vectors – such as an ANOVA design – and the \(x_{2i}\) are continuous random variables which may contain leverage points. Here \(M\) estimates are not robust, and \(S\) estimates may be too expensive. We propose two types of estimates: one is a weighted \(L_1\) estimate, and the other a combination of \(M\) and \(S\) estimates, which attains the maximum breakdown point. The consistency and asymptotic normality of both types of estimates are proved. Simulations suggest that the former is better when the dimension of \(x_{2i}\) is \(\leq 3\), and the latter when it is \(\geq 4\), especially for high contamination.

MSC:

62F35 Robustness and adaptive procedures (parametric inference)
62J05 Linear regression; mixed models
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