Novel properties of the objective function in both empirical and population settings of the least trimmed squares (LTS) regression (Rousseeuw 1984), along with other properties of the LTS, are established first time in this article. The primary properties of the objective function facilitate the establishment of other original results, including influence function and Fisher consistency. The strong consistency is established first time with the help of a generalized Glivenko-Cantelli Theorem over a class of functions. Differentiability and stochastic equicontinuity promote the re-establishment of asymptotic normality with a neat, concise, and novel approach.

翻译：本文首次建立了最小截断平方（LTS）回归（Rousseeuw 1984）在经验与总体设定下目标函数的新性质，以及LTS的其他性质。目标函数的主要性质有助于确立其他原创性结果，包括影响函数和Fisher一致性。借助广义Glivenko-Cantelli定理在一类函数上的应用，首次建立了强相合性。可微性和随机等度连续性通过一种简洁新颖的方法推动了渐近正态性的重新建立。