Least trimmed squares

On the other hand, least trimmed squares (LTS) can be used to estimate the calibration parameters that points which produce the (n — h) largest deviation squares are rejected and the remaining h points are used for the LTS fitting ... 

In Figure 6.2, a robust regression fit is superimposed. The least-trimmed squares estimator (LTS) proposed by Rousseeuw [7] is given by... 

The inspection of outliers is the next step in the statistical processing. In the presence of outliers, least squares estimation is biased. Nowadays a number of robust MLR methods are available to treat data that contain outliers (21), least trimmed squares being one of the many popular alternatives. Interestingly, in many QSRR studies, it is precisely the outliers that are of physicochemical interest. 

Least Trimmed sum of Squares (LTS) regression (Rousseeuw 1984) minimizes the sum of the smallest h squared residuals. Depending on the desired robustness, h can be varied between half and all the observations. 

Leaded Paint. The lead content of paint on the interiors of houses was determined by x-ray fluorescence analyzers. The same location was used in each room of each individual house. Fifty percent of the determinations were made on painted walls, and the other fifty percent were made on the trim paint. The precision of these instruments is +. 2 milligrams per square centimeter. Therefore, values of. 7 or greater are considered to represent at least 0.5 mg/cm. ... 

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