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arXiv · 1903.07850

Relative Efficiency of Higher Normed Estimators Over the Least Squares Estimator

Gopal K Basak·Samarjit Das·Arijit De·Atanu Biswas
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Abstract

In this article, we study the performance of the estimator that minimizes $L_{2k}- $ order loss function (for $ k \ge \; 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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Gopal K Basak, Samarjit Das, Arijit De, Atanu Biswas. 2019-03-19. Relative Efficiency of Higher Normed Estimators Over the Least Squares Estimator. https://arxiv.org/abs/1903.07850

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