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The least trimmed squares (LTS) estimator is popular in location, regression,machine learning, and AI literature. Despite the empirical version of leasttrimmed squares (LTS) being repeatedly studied in the literature, thepopulation version of the LTS has never been introduced and studied. The lackof the population version hinders the study of the large sample properties ofthe LTS utilizing the empirical process theory. Novel properties of theobjective function in both empirical and population settings of the LTS andother properties are established for the first time in this article. Theprimary properties of the objective function facilitate the establishment ofother original results, including the influence function and Fisherconsistency. The strong consistency is established with the help of ageneralized Glivenko-Cantelli Theorem over a class of functions for the firsttime. Differentiability and stochastic equicontinuity promote the establishmentof asymptotic normality with a concise and novel approach.

Large sample behavior of the least trimmed squares estimator