标题： 通过参数方法和连续性的半参数学 显示英文标题

标题： Semiparametrics via parametrics and contiguity

摘要： 对半参数模型的参数部分进行推断并不是一项简单的任务。 另一方面，如果用一个参数函数来近似半参数模型的无限维部分，就可以得到一个在某种意义上接近半参数模型的参数模型；并且可以通过最大似然方法进行推断。 在正则条件下，并假设近似参数模型实际上生成了数据，由此产生的最大似然估计量是渐近正态且有效的（在近似参数模型中）。 因此，我们得到了一系列渐近正态且有效的估计量，在一系列增长的参数模型中近似半参数模型，直观上，极限{`}半参数{'}估计量也应该渐近正态且有效。 在本文中，我们将这种直觉严格化。 因此，我们能够将许多半参数分析带回经典的参数领域，然后通过连续性将我们的参数结果翻译回半参数世界。 我们的方法不同于筛子文献，因为它更具体地描述了近似参数模型，在处理参数模型时是在这些模型下进行的，并且利用了参数模型和半参数模型之间的相互连续性，从而将关于前者的结果提升到关于后者的结果。 我们用两个半参数模型的经典例子来说明我们的理论，即部分线性回归模型和Cox回归模型。 我们的理论的一个结果是对Cox部分似然估计量效率的一种新的、相对简单且较为参数化的证明。 显示英文摘要

摘要： Inference on the parametric part of a semiparametric model is no trivial task. On the other hand, if one approximates the infinite dimensional part of the semiparametric model by a parametric function, one obtains a parametric model that is in some sense close to the semiparametric model; and inference may proceed by the method of maximum likelihood. Under regularity conditions, and assuming that the approximating parametric model in fact generated the data, the ensuing maximum likelihood estimator is asymptotically normal and efficient (in the approximating parametric model). Thus one obtains a sequence of asymptotically normal and efficient estimators in a sequence of growing parametric models that approximate the semiparametric model and, intuitively, the limiting {`}semiparametric{'} estimator should be asymptotically normal and efficient as well. In this paper we make this intuition rigorous. Consequently, we are able to move much of the semiparametric analysis back into classical parametric terrain, and then translate our parametric results back to the semiparametric world by way of contiguity. Our approach departs from the sieve literature by being more specific about the approximating parametric models, by working under these when treating the parametric models, and by taking advantage of the mutual contiguity between the parametric and semiparametric models to lift conclusions about the former to conclusions about the latter. We illustrate our theory with two canonical examples of semiparametric models, namely the partially linear regression model and the Cox regression model. An upshot of our theory is a new, relatively simple, and rather parametric proof of the efficiency of the Cox partial likelihood estimator.