ASYMPTOTICS OF THE REPEATED MEDIAN SLOPE ESTIMATOR

The influence function is determined for (twice) repeated median estim ators with arbitrary kernel functions, and more generally in the case where the two medians are replaced by a general class of estimators. A symptotic normality is then established for the repeated median estima tor of the slope parameter in simple linear regression. In this case t he influence function is hounded. For bivariate Gaussian data the effi ciency becomes 4/pi(2) approximate to 40.5%, which is the square of th e efficiency of the univariate median. The asymptotic results are comp ared with finite-sample efficiencies. It turns out that the convergenc e to the asymptotic behavior is extremely slow.