Least trimmed squares (LTS), or least trimmed sum of squares, is a robust statistical method that fits a function to a set of data whilst not being unduly affected by the presence of outliers[1] .
For a least trimmed squares analysis, this objective function is replaced by one constructed in the following way.
In this notation, the standard sum of squares function is while the objective function for LTS is Because this method is binary, in that points are either included or excluded, no closed-form solution exists.
As a result, methods for finding the LTS solution sift through combinations of the data, attempting to find the k subset that yields the lowest sum of squared residuals.
Methods exist for low n that will find the exact solution; however, as n rises, the number of combinations grows rapidly, thus yielding methods that attempt to find approximate (but generally sufficient) solutions.