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首页> 外文期刊>Quality & Quantity: International Journal of Methodology >Multicollinearity in regression: an efficiency comparison between L-p-norm and least squares estimators
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Multicollinearity in regression: an efficiency comparison between L-p-norm and least squares estimators

机译：回归中的多色性：L-P范数和最小二乘估计之间的效率比较

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摘要

Multicollinearity is one of the most important issues in regression analysis, as it produces unstable coefficients' estimates and makes the standard errors severely inflated. The regression theory is based on specific assumptions concerning the set of error random variables. In particular, when errors are uncorrelated and have a constant variance, the ordinary least squares estimator produces the best estimates among all linear estimators. If, as often happens in reality, these assumptions are not met, other methods might give more efficient estimates and their use is therefore recommendable. In this paper, after reviewing and briefly describing the salient features of the methods, proposed in the literature, to determine and address the multicollinearity problem, we introduce the L-pmin method, based on L-p-norm estimation, an adaptive robust procedure that is used when the residual distribution has deviated from normality. The major advantage of this approach is that it produces more efficient estimates of the model parameters, for different degrees of multicollinearity, than those generated by the ordinary least squares method. A simulation study and a real-data application are also presented, in order to show the better results provided by the L-pmin method in the presence of multicollinearity.
机译：多色性是回归分析中最重要的问题之一，因为它产生不稳定的系数估计，并使标准误差严重膨胀。回归理论基于关于误差随机变量集的具体假设。特别地，当错误不相关并且具有恒定方差时，普通的最小二乘估计器在所有线性估计器之间产生最佳估计。如果经常发生在现实中，则不满足这些假设，其他方法可能会提供更有效的估计值，因此它们的使用是推荐的。在本文中，在审查和简要描述文献中提出的方法的突出特征之后，要确定和解决多元性问题，我们介绍了基于LP-NOM估计的L-PMIN方法，是一种自适应强大的程序当残留分布偏离正常性时使用。这种方法的主要优点在于它产生的模型参数的更有效估计，用于不同的多色性的多型性，而不是由普通最小二乘法产生的那些。还提出了一种模拟研究和实数据应用，以便在多型原性存在下通过L-PMIN方法提供更好的结果。

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