Synergetic methods of data merging in mathematical statistics

Abstract

A comparative analysis of some aspects inherent in methods of mathematical statistics and synergetic methods of data complexation is carried out. The results obtained are used to increase the efficiency of statistical estimates computed from a small sample and also to determine estimates of characteristics of objects and processes in synergetic systems of data complexation when the number of channels is limited.A direction of investigation in the field of synergetics [1, 2] is the development of methods of data complexation (merging). In contrast to the general theory of systems, synergetics studies cooperative, coherent, and self-consistent processes running in complex systems. Whereas cybernetics develops control methods that provide the achievement of the formulated objective by a system owing to its functioning in a predetermined manner, synergetics organizes a process characterized by self-control and self-organization in accordance with the objective formulated. Here, complicated processes are developed not as a result of centralized actions but owing to the interaction of a collection of components. The cooperation of components makes it possible to use reserve capabilities of a system and to substantially increase the extent of system effect.In complex synergetic systems, information on the same process (an object or an event) is usually transmitted over several channels. The problem lies in determining the channels over which more significant data are transmitted. Depending on this, it is required to combine (integrate) obtained data to develop a cooperative decision on the state of an object. In the traditional method, it is expected that one or several most informative (dominant) channels are selected and that the other channels are truncated. This is realized by means of the mechanism of reducers of degrees of freedom [1]. An advantage of this method is its simplicity but some information contained in data received from the truncated channels drops out of consideration and does not participate in the process of development of a cooperative decision.In synthesizing a synergetic system of data complexation, it makes sense to refuse the conception of a dominant and, instead of reducers of degrees of freedom, to use discriminators of degrees of freedom, i.e., mechanisms that allow all the channels of obtaining data to participate in the process of formation of a decision with the weights corresponding to the degree of their informativeness in the current situation. As a result, all the items of available information will be used properly.The synergetic principle of data complexation has much in common with mathematical statistics [3]. In particular, the synergetic conception of data merging is applied to the estimation of characteristics of processes (objects) from an available data set, and mathematical statistics studies methods for estimation of moments of distribution of random quantities from an available collection of sample units. The commonality of problems of both theories testifies to the topica...

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