论文标题
近端估计和推理
Proximal Estimation and Inference
论文作者
论文摘要
我们构建了一个统一的凸分析框架，该框架表征了在规则和不规则设计下的大量惩罚估计器的统计特性。我们的框架将惩罚估计器解释为近端估计器，该估计值由应用于相应的初始估计器的近端操作员定义。我们表征了近端估计量的渐近特性，表明它们的渐近分布仅取决于（i）初始估计量的渐近分布，（ii）估计量极限亚级别的渐近分布和（iii）定义相关近端操作员的内部产品。同时，我们从其罚款亚级别的特性中表征了近端估计器的甲骨文特征。我们利用定期或不规则设计的系统性覆盖线性回归设置的方法。对于这些设置，我们构建了新的$ \ sqrt {n} - $一致，渐近地正常的无骑行型近端估计器，这些估计量具有Oracle属性，并显示出在实际相关的蒙特卡洛设置中令人满意的。
We build a unifying convex analysis framework characterizing the statistical properties of a large class of penalized estimators, both under a regular and an irregular design. Our framework interprets penalized estimators as proximal estimators, defined by a proximal operator applied to a corresponding initial estimator. We characterize the asymptotic properties of proximal estimators, showing that their asymptotic distribution follows a closed-form formula depending only on (i) the asymptotic distribution of the initial estimator, (ii) the estimator's limit penalty subgradient and (iii) the inner product defining the associated proximal operator. In parallel, we characterize the Oracle features of proximal estimators from the properties of their penalty's subgradients. We exploit our approach to systematically cover linear regression settings with a regular or irregular design. For these settings, we build new $\sqrt{n}-$consistent, asymptotically normal Ridgeless-type proximal estimators, which feature the Oracle property and are shown to perform satisfactorily in practically relevant Monte Carlo settings.
