Two Linear Programming Algorithms for Unbiased Estimation of Linear Models

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Abstract
Consider the estimation of in the familiar linear model . It is well-known that the least squares estimation principle yields an un-biased estimator . Two alternative estimation principles sometimes considered are the minimization of the sum of absolute residuals and the minimization of the maximum absolute residual. Since these alternative principles do not usually lead to a unique estimator, the latter depends on the computational algorithm used. We develop two algorithms which are based upon these alternative principles and yield unbiased estimators. The algorithms' essential features are the use of linear programming and an “antisymmetrical” initial estimator.

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