On the Second Order Behaviour of the Bootstrap of‎ L_1 Regression Estimators

We consider the second-order asymptotic properties of‎  ‎the bootstrap of L_1 regression estimators by looking at‎ ‎the difference between the L_1 estimator and ‎its first-order approximation‎, ‎where the latter‎ ‎is the minimizer of a quadratic approximation to the‎ ‎L_1 objective function‎. ‎It is shown that the bootstrap ‎distribution of the normed difference does not converge‎ ‎(either in probability or with probability 1)‎ ‎to the ``correct'' limiting distribution but rather converges ‎in distribution to a random distribution‎. ‎A characterization‎ ‎of this random distribution is given‎. ‎Some applications and extensions ‎are given.