Unbiased L1 and L∞ estimation

Sielken and Heartely 1973 have shown that the L₁ and L_∞ estimation problems may be formulated in such a way as to yield unbiased estimators of in the standard linear model y = Xβ + ε In this paper we will show that the L₁ estimation problem is closely related to the dual of the L_∞ estimation problem and vice versa. We will use this resu;t to obtain four fistiner lineat programming problems which yield unbiased L₁ and L_∞ estimators of β.