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L1 regression |
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matrix norming, central limit theorem, asymptotic distribution, generalized bootstrap |
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BOSE Arup |
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Article by BOSE Arup |
L1 regression estimate and its bootstrap
BOSE Arup
Statistics and Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India
We study the asymptotic distribution of the $L_1$ regression estimator under general conditions with matrix norming and possibly non i.i.d. errors. We then introduce an appropriate bootstrap procedure to estimate the distribution of this estimator and study its asymptotic properties. It is shown that this bootstrap is consistent under suitable conditions and in other situations the bootstrap limit is a random distribution.
This work was supported by J.C. Bose National Fellowship, Government of India