| Abstract: | Consider the estimation of [beta] in the familiar linear model y = X[beta] + e. It is well-known that the least squares estimation principle gives rise to an unbiased estimator [beta bar] under very mild conditions. Two alternative estimation principles sometimes considered are the minimization of the sum of absolute residuals and the maximum absolute residual. Since these principles will usually not lead to a unique estimator, the latter will depend on the linear programming algorithm used for its computation. We develop two algorithms which are based upon these alternative principles and yield, under very general conditions, unbiased estimators. The essential feature of these algorithms is the use of a readily obtainable, "antisymmetrical," initial estimator. This estimator allows the underlying linear programming problems to be represented in a symmetrical form. |
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