Abstract
Basic problems in the use of applied mathematical statistics for the modeling of complex systems are considered; the possibility of establishing the uniqueness of a mathematical model of optimal complexity by the group method of data handling (GMDH) is demonstrated. The basic shortcoming of contemporary mathematical statistics is that the models used are too simple because until now in regression analysis only one mean-squared error criterion has been used. To define a mathematical model of optimal complexity GMDH uses not one but two criteria and these two criteria assure a unique solution. The resulting equations are so complex that only the multilayered structure of GMDH allows us to write them down. The method works not only whenK ⩽N but also whenK >N(Kis the number of coefficients of the regression equation,N is the number of interpolation points). Increasing the area of optimization raises the accuracy of the model. The second criterion should be heuristic. Mean-squared error defined on a test sequence is used. The division of data into training and test sequences is the basic object of so-called “goal-directed regularization.” A second shortcoming of contemporary applied mathematical statistics is the absence of “freedom of decision” in the terminology of D. Gabor. The GMDH selection-type algorithm realizes both the self-organization and “freedom of decision” criteria. GMDH is a nonparametric procedure and does not require many of the concepts of mathematical statistics.
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Ivakhnenko, A.G. Problems of complex system modeling and applied mathematical statistics. International Journal of Computer and Information Sciences 2, 49–60 (1973). https://doi.org/10.1007/BF00987152
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DOI: https://doi.org/10.1007/BF00987152