A Method of Searching for Extreme Observations in a Problem of Fuzzy Regression
The study of statistical data for outliers is an urgent task of modern mathematics. The reliability of these methods directly affects the quality of the subsequent processing of statistical data sets and the adequacy of the resulting conclusions. In general, all available observations should be checked and compared with a certain numerical indicator. The further conclusion should be made by comparing these indicators among themselves.
In this paper, a technique to search for statistical outliers for one of the possible regression models based on the Chebyshev norm is considered. The proposed approach is based on the Legendre transformation, one of the known transformations used in the convex analysis. This algorithm allows us to refer to the group of statistical outliers for a set of observations and not for individual observations. This key point distinguishes this algorithm from the most of the commonly used algorithms. This way, the task can be solved in one pass with less required time. An example of the study of a sample for outliers is presented. The possibility to compare the obtained characteristics provides the opportunity to solve the problem for a different number of assumed extreme values.
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