论文标题
最小修剪正方形估计器的大样本行为
Large sample behavior of the least trimmed squares estimator
论文作者
论文摘要
修剪最小的正方形（LTS）估计器在位置，回归，机器学习和AI文献中很受欢迎。尽管在文献中反复研究了最小修剪正方形（LTS）的经验版本，但LTS的人口版本从未被引入和研究。缺乏人口版本阻碍了利用经验过程理论的LTS大型样本特性的研究。本文首次建立了在LT和其他特性的经验和人口设置中的目标函数的新型特性。目标函数的主要特性有助于建立其他原始结果，包括影响函数和Fisher一致性。强大的一致性是在首次在一类函数上的广义glivenko-cantelli定理的帮助下建立的。通过简洁而新颖的方法，不同的性能和随机等级促进了渐近正态性的建立。
The least trimmed squares (LTS) estimator is popular in location, regression, machine learning, and AI literature. Despite the empirical version of least trimmed squares (LTS) being repeatedly studied in the literature, the population version of the LTS has never been introduced and studied. The lack of the population version hinders the study of the large sample properties of the LTS utilizing the empirical process theory. Novel properties of the objective function in both empirical and population settings of the LTS and other properties are established for the first time in this article. The primary properties of the objective function facilitate the establishment of other original results, including the influence function and Fisher consistency. The strong consistency is established with the help of a generalized Glivenko-Cantelli Theorem over a class of functions for the first time. Differentiability and stochastic equicontinuity promote the establishment of asymptotic normality with a concise and novel approach.
