RESISTANT LINEAR MODEL FITTING METHODS BASED ON THE DESCENT THROUGH THE NODAL STRAIGHT LINES 

Tyrsin Alexander Nikolayevich, doctor of technical sciences, associate professor, head of sub-department of applied mathematics,
Ural power engineering Institute, Ural Federal University named after the first President of Russia B. N. Yeltsin,
E-mail: at2001@yandex.ru
Azaryan Alexan Arturovich, postgraduate student, Ural power engineering Institute, Ural Federal University named after
the first President of Russia B. N. Yeltsin, E-mail: a.a.azaryan@gmail.com 

519.237.5:519.24 

Background. When fitting linear models, in many cases one has to deal with stochastic inhomogeneity of the experimental data. This is manifested in violation of the assumptions of the Gauss-Markov theorem, in particular, observations can contain outliers.
Under the circumstances the estimation of the parameters of models is required to perform using resistant methods. Among them are the least absolute deviations method and the generalized method of the least absolute deviations. However, the known algorithms for their implementation are sufficiently effective only for small dimensions of models and a limited sample size. The purpose of this study is the development of effective computational algorithms for the implementation of these methods, which have no limitations on the
order of the models and the amount of experimental data.
Materials and methods. The implementation of the tasks was achieved by the descent to the solution through the nodal
straight lines. To reduce computational costs, the feature of nodal straight lines is used – all nodes located on each such straight line are intersections of a set of hyperplanes, of which only one hyperplane is different.
Results. A review of known methods for realizing the least absolute deviations method and the generalized method of the least absolute deviations is given. The algorithms of descent through the nodal straight lines are described, which allow to significantly reduce the computational costs when implementing these methods. The achievement of a minimum in a finite number of steps when implementing the method of the least absolute deviations based on descent through the nodal straight lines is proved.
The implementation of the generalized method of the least absolute deviations by descent through the nodal straight lines allows us to find a global minimum or a solution close to it.
Conclusions. Effective algorithms for realization of the least absolute deviations method and the generalized method of the least absolute deviations when estimating the parameters of linear models based on descent through the nodal straight lines are proposed. The computational complexity of these algorithms makes possible their practical implementation for the analysis of experimental data and the construction of multidimensional linear models. 

least absolute deviations method, generalized method, linear model, regression, algorithm, nodal point, nodal straight line, hyperplane