Bauman Moscow State Technical University
Author list of organization
List of articles written by the authors of the organization
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DISTANCES IN THE SPACES OF STATISTICAL DATA
01.00.00 Physical-mathematical sciences
DescriptionThe core of applied statistics is statistics in spaces of arbitrary nature, based on the use of distances and optimization problems. This article discusses the various distances in spaces of statistical data, in particular, their conclusions on the basis of appropriate systems of axioms. The conditions and proofs of theorems first published in scientific periodicals
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THEORETICAL TOOLS OF STATISTICAL METHODS
01.00.00 Physical-mathematical sciences
DescriptionWe have considered the basic mathematical tools (theorems, methods) which are used regularly in the justification of new results in the field of statistical methods: rules of large numbers, central limit theorems, the necessary and sufficient conditions for the inheritance of convergence, the linearization method, the invariance principle
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01.00.00 Physical-mathematical sciences
DescriptionLusian - dichotomous data model as a finite sequence of independent Bernoulli trials with, generally speaking, different probabilities of success. The tasks of statistical hypothesis testing, classification, averaging lusians are discussed. In accordance with the requirements of practice the problems are considered primarily in the asymptotic behavior of increasing dimension, in which the number of unknown parameters increases in proportion to the size of data. The method of testing hypotheses on set of small samples and the theory of unbiased statistical estimates were proved to be useful
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SCIENCE AS THE OBJECT OF MANAGEMENT
DescriptionScience is considered as a branch of the national economy. We discuss the relationship of areas of human activity, applied science and fundamental science. As an example, the development of the fundamental theory of decision-making and expertise are considered in the implementation of applied researches in the aviation and rocket-space industry. Is emphasized that the major achievement in science - the novelty of the results. We discuss the problem of estimation the effectiveness of scientific activity, the advantages and disadvantages of estimates based on bibliometric databases and citation indices, we show the basic role of expert technologies. Is examined the role of globalization and patriotism in the development of science. Is substantiated the principal difference between acquiring knowledge and promote research results. We consider it necessary to conduct detailed studies into the science of science and development based on these science-based recommendations for the management of science
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A NEW APPROACH TO THE STUDY OF THE STABILITY OF CONCLUSIONS IN THE MATHEMATICAL MODELS
01.00.00 Physical-mathematical sciences
DescriptionWe have proposed the general scheme for studying the stability of the conclusions obtained by mathematical methods and models regarding tolerance deviations of the original data and background models. The concrete problems of stability are discussed: towards a change of data, its size and distributions, to allowable transformations measurement scales, to the temporal characteristics (time of start of the project, the planning horizon). Reducing the uncertainty can be conducted by changing the type of data, i.e. with the aid of the transition to non-numerical data. The models of concrete management processes of industrial organizations are considered on the examples of stability characteristics of investment projects to change the discount factors and in models of inventory management to change in the coefficients of the model and batch size production
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PROBABILISTIC-STATISTICAL METHODS IN GNEDENKO’S RESEARCHES
01.00.00 Physical-mathematical sciences
DescriptionWe analyze the probabilistic-statistical methods in the researches of Boris Vladimirovich Gnedenko – the academician of Ukrainian Academy of Science, which are very important for the XXI century. We have also discussed the limit theorems of probability theory, mathematical statistics, reliability theory, statistical methods of quality control and queuing theory. We give some information about the main stages of scientific career of B.V. Gnedenko, his views on the history of mathematics and teaching
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LIMIT THEORY OF NONPARAMETRIC STATISTICS
01.00.00 Physical-mathematical sciences
DescriptionWe have studied the asymptotic behavior of a broad class of nonparametric statistics, which includes statistics of omega-square type and Kolmogorov-Smirnov type. Limit theorems have been proved. We have also developed the method of approximation with step functions. With the help of this method we have obtained a number of necessary and sufficient conditions
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ABOUT CONTROLLING OF SCIENTIFIC ACTIVITY
DescriptionWe have selected the new area of controlling - scientific activity controlling. We consider some problems of development in this field, primarily the problem of selection of key performance indicators. It’s been founded that administrative measures stimulated the pursuit of a number of articles published in scientific journals hinders the development of science. Methodological errors - emphasis on citation indexes, impact factors, etc. - lead to wrong management decisions. As the experience of the UK, an expertise should be applied in the management of science. The article briefly discusses some of the drawbacks of the system of scientific specialties. It is proposed to expand research on the science of science and scientific activity controlling. We have also discussed the problems of controlling in applied research organizations
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PREDICTIVE POWER – THE BEST INDICATOR OF THE QUALITY OF THE DIAGNOSTIC ALGORITHM
01.00.00 Physical-mathematical sciences
DescriptionInexpediency of use of probability of correct diagnostics as a quality indicator of diagnostic algorithm is shown. The new indicator - the prognostic strength based on Mahalanobis distance between classes is offered and studied. We have found asymptotic distribution of the prognostic strength; the way of testing of adequacy of its application has been specified. In a problem of testing of two simple hypotheses the prognostic strength connection is established with Hellinger distance
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ESTIMATES OF PROBABILITY DENSITY FUNCTION IN SPACES OF ARBITRARY NATURE
01.00.00 Physical-mathematical sciences
DescriptionLinear estimators of the probability of density in the spaces of an arbitrary nature and particular cases – nuclear, histogram, the Fix-Hodges type estimates are introduced. Consistency and asymptotic normality of linear estimates are proved under natural conditions. It is shown that the probability of the area can be found by linear density estimates. A special case of a finite set are discussed, it was found that sample mode converges to the theoretical one