On UnbiasedLpRegression Estimators

Abstract

Consider the familiar linear model y = X β + e. In an ingenious article by Sielken and Hartley (1973) it was shown how one can construct a computational scheme that will generate unbiased L 1 or L ∞ estimators even when multiple solutions exist. In a recent paper, Harvey (1978) provides a simple proof of unbiasedness for L p estimators, 1 < p < ∞, under the assumption that the linear model is of full column rank; this insures that the estimator is unique. In this note it is shown that Sielken and Hartley's computational scheme can be extended to include unbiased L p estimators, p ≥ 1, without requiring a rank condition.