Abstract
Consider the standard linear model where x x ,x 2 … are assumed to be the known p-vectors, β the unknown p-vector of regression coefficients, and e 1 , e 2 , …the independent random error sequence, each having a median zero. Define the minimum L 1 norm estimator as,the solution of the minimization problem inf It is proved in this paper that is asymptotically normal under very weak conditions. In particular, the condition imposed on {xi} is exactly the same which ensures the asymptotic normality of least-squares estimate:
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