We consider inference about a scalar coefficient in a linear regression model. One previously considered approach to dealing with many controls imposes sparsity, that is, it is assumed known that nearly all control coefficients are (very nearly) zero. We instead impose a bound on the quadratic mean of the controls' effect on the dependent variable, which also has an interpretation as an R²‐type bound on the explanatory power of the controls. We develop a simple inference procedure that exploits this additional information in general heteroskedastic models. We study its asymptotic efficiency properties and compare it to a sparsity‐based approach in a Monte Carlo study. The method is illustrated in three empirical applications.

中文翻译：

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线性回归，许多控件的解释力有限

我们考虑在线性回归模型中关于标量系数的推断。一种先前考虑的处理许多控件的方法具有稀疏性，也就是说，假定已知几乎所有的控制系数都是（非常接近）零。我们取而代之的是，对控件对因变量的影响的二次均值强加一个界限，该平均值也被解释为对控件的解释力的R ²型界限。我们开发了一个简单的推理程序，该程序在一般的异方差模型中利用了这些附加信息。我们研究了它的渐近效率特性，并将其与基于蒙特卡洛研究的基于稀疏性的方法进行比较。在三个经验应用中说明了该方法。