论文标题
在高斯近似M-估计器上
On Gaussian Approximation for M-Estimator
论文作者
论文摘要
这项研究开发了一种用于M估计剂的分布的非质子高斯近似理论，该理论被定义为经验标准函数的最大化体。在现有的数学统计文献中，许多研究集中在近似M估计量的统计推断中的分布。与现有的方法主要集中在限制行为上相反，本研究采用了一种非反应方法，为经验标准的最大化器建立了抽象的高斯近似结果，并提出了高斯乘数自举近似方法。我们的发展可以被视为开创性作品的扩展（Chernozhukov，Chetverikov和Kato（2013，2014，2015））在近似理论上，用于对最大化者的经验过程分布。通过这项工作，我们为M估计量的统计理论开发了新的灯光。我们的理论不仅涵盖了常规估计器，例如最小绝对偏差，还涵盖了难以得出或在数值上近似限制分布（例如非donsker类和立方体根估计器）的某些非规范案例。
This study develops a non-asymptotic Gaussian approximation theory for distributions of M-estimators, which are defined as maximizers of empirical criterion functions. In existing mathematical statistics literature, numerous studies have focused on approximating the distributions of the M-estimators for statistical inference. In contrast to the existing approaches, which mainly focus on limiting behaviors, this study employs a non-asymptotic approach, establishes abstract Gaussian approximation results for maximizers of empirical criteria, and proposes a Gaussian multiplier bootstrap approximation method. Our developments can be considered as extensions of the seminal works (Chernozhukov, Chetverikov and Kato (2013, 2014, 2015)) on the approximation theory for distributions of suprema of empirical processes toward their maximizers. Through this work, we shed new lights on the statistical theory of M-estimators. Our theory covers not only regular estimators, such as the least absolute deviations, but also some non-regular cases where it is difficult to derive or to approximate numerically the limiting distributions such as non-Donsker classes and cube root estimators.
