Abstract

A simulation study is done to compare Ridge Regression (RR) and the Lasso, under the assumption of a linear model, by calculating four metrics: the squared distance, from the true coefficients, of estimated coefficients that are both statistically significant and true; the proportion of true regressors discovered; the squared distance, from the true predictions, of the predictions made using the estimated coefficients that are only statistically significant (but not necessarily true); and the chance that no estimated coefficient is true. Results indicate that RR surpasses the Lasso in regard to all of these metrics. This indicates that RR can add value to model discovery, in Economics and the Sciences, by continuing to employ the key concept of statistical significance in the classical sense to find true regressors. This is important, because it allows the “manufacturer” of models to focus on the process generating the data, if indeed there is one. And, thus, provide important feedback on the outputs of other fashionable competitors, such as Machine Learning, with their pervasive “black-box” focus on prediction as an end in itself.

摘要

在线性模型的假设下，通过计算四个指标来比较岭回归 (RR) 和 Lasso 进行了一项模拟研究： 与真实系数的平方距离，以及具有统计显着性和真实性的估计系数；发现的真正回归变量的比例；使用仅在统计上显着（但不一定为真）的估计系数做出的预测与真实预测的平方距离；以及没有估计系数为真的可能性。结果表明，在所有这些指标方面，RR 都超过了 Lasso。这表明 RR 可以通过继续使用经典意义上的统计显着性关键概念来找到真正的回归器，从而为经济学和科学中的模型发现增加价值。这个很重要，生成数据的过程，如果确实有的话。因此，为其他时尚竞争对手的输出提供重要的反馈，例如机器学习，他们普遍的“黑盒”专注于预测本身。