BOOTSTRAP METHODS FOR MEDIAN REGRESSION-MODELS

The least-absolute-deviations (LAD) estimator for a median-regression model does not satisfy the standard conditions for obtaining asymptoti c refinements through use of the bootstrap because the LAD objective f unction is not smooth. This paper overcomes this problem by smoothing the objective function. The smoothed estimator is asymptotically equiv alent to the standard LAD estimator. With bootstrap critical values, t he rejection probabilities of symmetrical t and chi(2) tests based on the smoothed estimator are correct through O(n(-gamma)) under the null hypothesis, where gamma < 1 but can be arbitrarily close to I. In con trast, first-order asymptotic approximations make errors of size O(n(- gamma)). These results also hold for symmetrical t and chi(2) tests fo r censored median regression models.