标题： 混合速率渐近性 显示英文标题

标题： Mixed-rates asymptotics

摘要： 提出了一种通用方法来推导定义为经验准则函数优化参数值的估计量的极限行为。这类估计量的渐近行为通常从按比例缩放和重参数化后的准则函数的一致极限定理中推导得出。新方法可以处理标准方法无法得到估计量完整极限行为的情况。渐近分析依赖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例子加以说明。 显示英文摘要

摘要： 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.