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.
Knight,K. (2022). On the Second Order Behaviour of the Bootstrap of L_1 Regression Estimators. Journal of the Iranian Statistical Society, 2(1), 21-42.
MLA
Knight,K. . "On the Second Order Behaviour of the Bootstrap of L_1 Regression Estimators", Journal of the Iranian Statistical Society, 2, 1, 2022, 21-42.
HARVARD
Knight K. (2022). 'On the Second Order Behaviour of the Bootstrap of L_1 Regression Estimators', Journal of the Iranian Statistical Society, 2(1), pp. 21-42.
CHICAGO
K. Knight, "On the Second Order Behaviour of the Bootstrap of L_1 Regression Estimators," Journal of the Iranian Statistical Society, 2 1 (2022): 21-42,
VANCOUVER
Knight K. On the Second Order Behaviour of the Bootstrap of L_1 Regression Estimators. JIRSS, 2022; 2(1): 21-42.
Journal of the Iranian Statistical Society