Keith Knight ^{}

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.

Received: 2011/08/25 | Accepted: 2015/09/12 | Published: 2003/03/15

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