Relative Efficiency of Higher Normed Estimators Over the Least Squares Estimator
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In this article, we study the performance of the estimator that minimizes L_2k- order loss function (for k > 2 ) against the estimators which minimizes the L_2- order loss function (or the least squares estimator). Commonly occurring examples illustrate the differences in efficiency between L_2k and L_2 - based estimators. We derive an empirically testable condition under which the L_2k estimator is more efficient than the least squares estimator. We construct a simple decision rule to choose between L_2k and L_2 estimator. Special emphasis is provided to study L_4 estimator. A detailed simulation study verifies the effectiveness of this decision rule. Also, the superiority of the L_2k estimator is demonstrated in a real life data set.
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