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Тезисы докладов

Задачи поддержки принятия решений

The paper deals with the censoring approach to the modeling and optimization of the robust function estimation. As a model of unknown dependence which needs to be restored nonparametrical regression one assumed. To make process independent on information about outliers and to achieve the best possible quality of the sample refinement the special criterions were formalized. As a rule, the experimental data which are the sample from some general unity with the "typical" observations include outliers which are about 10-15% of data volume. Outliers cause heavy tails of distributions of observations errors and disturbs the optimal condition for classical methods of the restorating of unknown function. Then there is real interest to the robust statistical methods, which is stable to such disturbance. The analysis of known methods allows to make following conclusion. All methods can be divided in to two classes. There are methods in the spirit of the Huber approach and the other type of the methods is based on the censoring of the learning sample. A priory information (such as distribution of the discrepancies, shape of the true function, numbers of outliers and so on) plays the main role in all the methods. So the quality of the robust estimation are determined by the corresponding of the sample features to this prescribed conditions. Besides it is necessary that the outliers be in a sample. Therefore such algorithms are the particular solutions only, but its not pretend to be of universal type. So it is naturally to claim, that 1) robust procedure to be independent from a priory information of specified type, and 2) outliers identification must be done in accordance to the formalized criterion of the quality which must be the function of the learning sample. On the strength of such specification the idea of the censoring methods is more proper. It is proposed to solve the task in the class of nonparametrical estimations. The property of local approximation of the last one is the flexible instrument which allows to formalize the specified requirements.

Примечание. Тезисы докладов публикуются в авторской редакции

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