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.

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