Bauman Moscow State Technical University
Author list of organization
List of articles written by the authors of the organization
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KEY STAGES OF STATISTICAL METHODS DEVELOPMENT
01.00.00 Physical-mathematical sciences
DescriptionThe first statistical publication – the Fourth Book of Moses, “Numbers” in the Old Testament. We trace the development of ideas about the statistics until the twentieth century. The present stage of statistical methods began with parametric statistics by Pearson, Student, Fisher. Scientometrics of statistical researches provides an indication of the accumulated results. Nonparametric statistics appeared in the 1930s, applied statistics in our country - at the turn of 1970-80. We have discussed what gives applied statistics to national economy. Also we have told briefly about the history of statistical methods in Russia (until Kolmogorov's time)
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RUSSIAN SCIENTIFIC SCHOOL IN THE ECONOMETRICS FIELD
01.00.00 Physical-mathematical sciences
DescriptionWe have considered the formation of the Russian scientific school in the field of econometrics, obtained its obtained scientific results, the possibilities of their use in solving problems of the economy, the organization of production and controlling of industrial companies and organizations, as well as in teaching. As econometrics we consider a scientific and an academic discipline devoted to the development and application of statistical methods to study economic phenomena and processes, in short, statistical methods in economics. Therefore, we can say that a lot of domestic books and articles, in particular, the works by the author of this publication from the beginning of the 70s, are the parts of econometrics. However, in this article we consider only the works, in the titles of which we can see the word of "econometrics". In our country the term "econometrics" has become popular since the mid 90s. However, many publications and training courses are still developed in the western outdated paradigm. They do not conform to the new paradigm of mathematical methods of economics, the new paradigm of applied statistics and mathematical statistics, mathematical methods of research. Russian science school in the field of econometrics operates within the scientific school in the field of probability theory and mathematical statistics based by A.N. Kolmogorov. Russian science school is developed in accordance with the new paradigm of mathematical methods. It is necessary to examine the main results of Russian scientific schools in the field of econometrics. We present the information on the institutional design of national scientific schools in econometrics, in particular, on the activities of the Institute of High Technologies statistics and econometrics
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01.00.00 Physical-mathematical sciences
DescriptionAccording to the new paradigm of applied mathematical statistics one should prefer non-parametric methods and models. However, in applied statistics we currently use a variety of parametric models. The term "parametric" means that the probabilistic-statistical model is fully described by a finite-dimensional vector of fixed dimension, and this dimension does not depend on the size of the sample. In parametric statistics the estimation problem is to estimate the unknown value (for statistician) of parameter by means of the best (in some sense) method. In the statistical problems of standardization and quality control we use a three-parameter family of gamma distributions. In this article, it is considered as an example of the parametric distribution family. We compare the methods for estimating the parameters. The method of moments is universal. However, the estimates obtained with the help of method of moments have optimal properties only in rare cases. Maximum likelihood estimation (MLE) belongs to the class of the best asymptotically normal estimates. In most cases, analytical solutions do not exist; therefore, to find MLE it is necessary to apply numerical methods. However, the use of numerical methods creates numerous problems. Convergence of iterative algorithms requires justification. In a number of examples of the analysis of real data, the likelihood function has many local maxima, and because of that natural iterative procedures do not converge. We suggest the use of one-step estimates (OS-estimates). They have equally good asymptotic properties as the maximum likelihood estimators, under the same conditions of regularity that MLE. One-step estimates are written in the form of explicit formulas. In this article it is proved that the one-step estimates are the best asymptotically normal estimates (under natural conditions). We have found OS-estimates for the gamma distribution and given the results of calculations using data on operating time to limit state for incisors
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ESTIMATION OF INFLATION ON THE BASIS OF INDEPENDENT INFORMATION
DescriptionThis article is devoted to the investigations of our research team built for independent collection and examination the information about prices, ie to study the real inflation. The approach to measuring the rise in prices is based on selecting and fixing tool of economists and managers - the consumer basket which does not change during the time. On the basis of physiological consumption norms of the Institute of Nutrition (Russian Academy of medical Sciences) we made up the minimum consumer basket, ie we set annual consumption on food staples required to maintain normal functioning of the human body. In 1993-2015 we carried out an independent price collection. We obtained values of the consumer basket and inflation indices. We give the comparison with the data of official statistics. Our work is aimed at the elimination of Rosstat's monopoly in calculating the index of inflation, the minimum subsistence level and the real disposable income of the population. Using the same consumer basket makes it possible to compare the results of calculations for different time periods. That is why our works compare favorably to the approach of the official statistics. We have given a more detailed analysis of inflation in the XXI century. We have also briefly reviewed the use of inflation indices in the analysis of problems of households, organizations and production firms, as well as the country as a whole
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Description
Estimates of the errors of the characteristics of financial flows of investment projects are needed to make adequate management decisions, particularly in the rocket and the space industry. Organizational-economic approaches to the estimations of the feasibility of innovation-investment projects to create rocket and space technologies require intensive use of numerical characteristics of the financial flows of long-term projects of this type. In organizational-economic support for control problems in the aerospace industry we must provide the need to obtain the estimates of the errors of the characteristics of financial flows. Such estimates are an integral part of the organizational-economic support of innovation activity in the aerospace industry. They can be compared with the predictions interval, i.e. confidence estimation of predictive values. Half the length of the confidence interval is the prediction error estimate. In this article we give the new method for estimating the errors of the main characteristics of the investment projects. We focus on the net present value called NPV. Our method of estimation of errors is based on the results of statistics interval data, which is an integral part of the system fuzzy interval mathematics. We construct asymptotic theory which corresponds to small deviations of discount coefficients. The error of NPV has been found as the asymptotic notna. With up to infinitesimals of higher orders the error of NPV is a linear function of the maximum possible error of discount coefficients
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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
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Description
The analysis of social and economic development of countries in the conditions of the globalization of the world economy which is carried out with the use of thermo-dynamical model showed that interaction of the open economic systems standing on different levels of development can lead to absorption or destruction of one systems by others that finally will lead to "thermal death" in economy (stagnation). The closed economic systems can communicate with other countries by means of international trade. Less developed countries can't compete with industrially developed states and will inevitably get under their influence. The isolated economic systems can develop only in the presence of domestic market, resources and rigid social structure. Introduction of the anti-Russian sanctions and other external factors led to restriction of the influence of the foreign capital. Innovative activity in economy and strengthening of government institutions might be observed as a result. The thermo-dynamical model shows that partial isolation of the developing economic system possessing sufficient production and scientific potential leads to stabilization of its structure and growth of the innovative activity
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CONSEQUENCES OF DECISIONS FOR SCIENCE-TECHNOLOGY AND ECONOMIC DEVELOPMENT
DescriptionThe real facts presented in this article, demonstrate the great importance in today's world of strategic management, methods of analyses of innovations and investments and the role of the theory of decision-making in these economic disciplines. We have given the retrospective analysis of the development of nuclear physics research. For the development of fundamental and applied science in the second half of the twentieth century, we had a very great importance of the two events: the decision of US President Roosevelt to deploy nuclear program (adopted in response to a letter from Einstein) and the coincidence in time between the completion of the construction of nuclear bomb and the end of World War II. The nuclear bombing of Hiroshima and Nagasaki has determined the developments in science and technology for the entire second half of the twentieth century. For the first time in the entire history of the world the leaders of the leading countries clearly seen that fundamental research can bring great practical benefit (from the point of view of the leaders of countries). Namely, they can give the brand new super-powerful weapon. The consequence was a broad organizational and financial support of fundamental and deriving from them applied research. Is analyzed the influence of fundamental and applied research on the development and effective use of new technology and technical progress. We consider the development of mathematical methods of research and information technology, in particular, the myth of "artificial intelligence"
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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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THE LIMIT THEORY OF THE SOLUTIONS OF EXTREMAL STATISTICAL PROBLEMS
01.00.00 Physical-mathematical sciences
DescriptionMany procedures of applied mathematical statistics are based on the solution of extreme problems. As examples it is enough to name methods of least squares, maximum likelihood, minimal contrast, main components. In accordance with the new paradigm of applied mathematical statistics, the central part of this scientific and practical discipline is the statistics of non-numerical data (it is also called the statistics of objects of non-numerical nature or non-numeric statistics) in which the empirical and theoretical averages are determined by solving extreme problems. As shown in this paper, the laws of large numbers are valid, according to which empirical averages approach the theoretical ones with increasing sample size. Of great importance are limit theorems describing the asymptotic behavior of solutions of extremal statistical problems. For example, in the method of least squares, selective estimates of the parameters of the dependence approach the theoretical values, the maximum likelihood estimates tend to the estimated parameters, etc. It is quite natural to seek to study the asymptotic behavior of solutions of extremal statistical problems in the general case. The corresponding results can be used in various special cases. This is the theoretical and practical use of the limiting results obtained under the weakest assumptions. The present article is devoted to a series of limit theorems concerning the asymptotics of solutions of extremal statistical problems in the most general formulations. Along with the results of probability theory, the apparatus of general topology is used. The main differences between the results of this article and numerous studies on related topics are: we consider spaces of a general nature; the behavior of solutions is studied for extremal statistical problems of general form; it is possible to weaken ordinary requirements of bicompactness type by introducing conditions of the type of asymptotic uniform divisibility