Author

• Keith Knight

Abstract

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.

Keywords

• Bahadur-Kiefer representations
• ‎ ‎bootstrap
• L_1 estimation
• linear regression