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Asymptotics of the repeated median slope estimator. (English) Zbl 0817.62018
Summary: The influence function is determined for (twice) repeated median estimators with arbitrary kernel functions, and more generally in the case where the two medians are replaced by a general class of estimators. Asymptotic normality is then established for the repeated median estimator of the slope parameter in simple linear regression. In this case the influence function is bounded. For bivariate Gaussian data the efficiency becomes $$4/ \pi^ 2 \approx 40.5 \%$$, which is the square of the efficiency of the univariate median. The asymptotic results are compared with finite-sample efficiencies. It turns out that the convergence to the asymptotic behavior is extremely slow.

##### MSC:
 62F12 Asymptotic properties of parametric estimators 62F35 Robustness and adaptive procedures (parametric inference) 62J05 Linear regression; mixed models
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