Despite the empirical version of least trimmed squares (LTS) in regression (Rousseeuw \cite{R84}) having been repeatedly studied in the literature, the population version of LTS has never been introduced. Novel properties of the objective function in both empirical and population settings of the LTS, along with 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. Differentiability and stochastic equicontinuity promote the establishment of asymptotic normality with a concise and novel approach.

翻译：尽管回归分析中最小修剪平方（LTS）的经验版本（Rousseeuw \cite{R84}）已在文献中被反复研究，但其总体版本却从未被引入。本文首次建立了LTS在经验设置与总体设置中目标函数的新性质及其他特性。目标函数的主要性质有助于确立其他原创性结果，包括影响函数与Fisher一致性。借助一类函数上的广义Glivenko-Cantelli定理，建立了强相合性。可微性与随机等度连续性通过一种简洁新颖的方法促进了渐近正态性的建立。