Volume 2, Number 1 (2003) | JIRSS 2003, 2(1): 21-42 | Back to browse issues page


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Knight K. On the Second Order Behaviour of the Bootstrap of‎ L_1 Regression Estimators . JIRSS. 2003; 2 (1) :21-42
URL: http://jirss.irstat.ir/article-1-92-en.html

Abstract:   (6862 Views)
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.
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Subject: 60: Probability theory and stochastic processes
Received: 2011/08/25 | Accepted: 2015/09/12

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