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The asymptotics of S-estimators in the linear regression model. (English) Zbl 0719.62042
The asymptotic behaviour of the least median of squares estimator in the linear regression model is studied. A weak convergence theorem for the estimator is given and it is shown under rather general conditions that the correct norming factor is $$n^{1/3}$$. The asymptotic normality of S- estimators is obtained under weak conditions on the carriers.

##### MSC:
 62F12 Asymptotic properties of parametric estimators 62J05 Linear regression; mixed models 60F05 Central limit and other weak theorems
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