In this paper; the L1 -norm estimators and the random weighted statistic for a semiparametric regression model are constructed; the strong convergence rates of estimators are obtain under certain conditions; the strong eciency of the random weighting method is shown. A simulation study is conducted to compare the L1 -norm estimator with the least square estimator in term of approximate accuracy; and simulation results are given for comparison between the random weighting method and normal approximation method.