Mixed-rates asymptotics
Mixed-rates asymptotics
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混合率渐进
DOI：
10.1214/009053607000000668
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
P. Radchenko
中科院分区：
文献类型：
--
作者：
P. Radchenko
提出了一种用于推导估计器限制行为的通用方法，估计器被定义为优化经验准则函数的参数值。这种估计器的渐近行为通常是根据重新调整和重新参数化的准则函数的统一极限定理推导出来的。新方法可以处理标准方法不能产生估计器的完整限制行为的情况。渐近分析取决于将准则函数分解为具有不同缩放比例的分量之和。该方法通过 Lasso 型估计、$k$ 均值聚类、Shorth 估计和部分线性模型的示例进行解释。
A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from uniform limit theorems for rescaled and reparametrized criterion functions. The new method can handle cases where the standard approach does not yield the complete limiting behavior of the estimator. The asymptotic analysis depends on a decomposition of criterion functions into sums of components with different rescalings. The method is explained by examples from Lasso-type estimation, $k$-means clustering, Shorth estimation and partial linear models.