Universal sieve-based strategies for efficient estimation using machine learning tools.
Universal sieve-based strategies for efficient estimation using machine learning tools.
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DOI：
10.3150/20-bej1309
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发表时间：
2021-11
期刊：
影响因子：
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通讯作者：
Carone M
中科院分区：
文献类型：
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作者：
Qiu H;Luedtke A;Carone M
假设我们希望在非参数模型下估计底层数据生成机制的一个或多个函数值特征的有限维摘要。估计的一种方法是插入这些特征的灵活估计。不幸的是，在一般情况下，这样的估计可能不是渐近有效的，这往往使这些估计难以作为推理的基础。虽然有几个现有的方法来构建渐近有效的插件估计，每一个这样的方法要么只能使用效率理论的知识，或仅在严格的平滑假设下是有效的。在现有的方法中，筛估计脱颖而出，特别方便，因为效率理论是不需要在他们的建设，他们的调整参数可以选择自适应的数据，他们是普遍的意义上说，同样的适合导致有效的插件估计丰富的一类被估量。受这些理想属性的启发，我们提出了两种新的通用方法来估计函数值的功能，可以使用筛估计理论进行分析。与传统的筛估计相比，这些方法在更一般的条件下是有效的函数值特征的平滑度，通过利用灵活的估计，可以获得，例如，使用机器学习。
Suppose that we wish to estimate a finite-dimensional summary of one or more function-valued features of an underlying data-generating mechanism under a nonparametric model. One approach to estimation is by plugging in flexible estimates of these features. Unfortunately, in general, such estimators may not be asymptotically efficient, which often makes these estimators difficult to use as a basis for inference. Though there are several existing methods to construct asymptotically efficient plug-in estimators, each such method either can only be derived using knowledge of efficiency theory or is only valid under stringent smoothness assumptions. Among existing methods, sieve estimators stand out as particularly convenient because efficiency theory is not required in their construction, their tuning parameters can be selected data adaptively, and they are universal in the sense that the same fits lead to efficient plug-in estimators for a rich class of estimands. Inspired by these desirable properties, we propose two novel universal approaches for estimating function-valued features that can be analyzed using sieve estimation theory. Compared to traditional sieve estimators, these approaches are valid under more general conditions on the smoothness of the function-valued features by utilizing flexible estimates that can be obtained, for example, using machine learning.