The article considers provisions of axiomatic theory of Fisher indices, which is an important part of modern theory of price statistics and GDP international comparisons based on purchasing power parities. International recommendations concerning the computation of CPI and international comparisons of GDP, proposing different index formulas, are based on provisions of axiomatic theory although some require- ments for index formulas are not consistent with each other. The Fisher index formula meets time reversal and factor reversal requirements but fails to meet additivity and transitivity requirements and for these reasons cannot be used for multilateral comparisons of GDP. Most im- portantly, many experts in index theory believe that Fisher index does not have economic foundation. It is noted that axiomatic theory does not deal with many important problems of price statistics and represents the result of application of formal mathematical approach. Nevertheless, it is useful to take into account the provisions of this theory when interpreting recommended and published index formulas.

The authors studied heterogeneous samples (for a number of statistical populations) taken from finite mixtures of probability distribu- tions, which reflect a number of socio-economic characteristics of the Russian society, using the information resources of the Federal State Statistics Service; in this case the number of mixing distributions (components), as well as their corresponding weights and parameters, may be unknown. In terms of content, the problem of separation (decomposition) of mixtures can be reduced to estimating unknown parameters of mixing distributions and their weights.
The article considers and discusses methods for solving this problem, their advantages and disadvantages, conditions and areas of application. In the study the decomposition of mixtures of probability distributions on the population of subjects of the Russian
Federation was carried out according to three interrelated statistical indicators – the unemployment rate, the poverty rate, the level of violence. These indicators can be considered as statistical measure of achieving sustainable development goals at the regional level and, at the same time, measures of socio-economic «health» of territory. Typologies of subjects of the Russian Federation were carried out according to the listed indicators. A cross-comparison of the results of the obtained typological groupings was performed, which also made it possible to identify the subjects of the Russian Federation that differ in both negative and positive trends in the context of the indicators under consideration.
The authors underline that the results of the study can be used by the authorities to develop specific measures for the socio-economic development of Russia and its regions.

It is noted that before the adoption of unprecedented Western sanctions under the pretext of launching a special military operation, the Rus- sian economy had achieved relatively high macro indicators of development. Based on the analysis of the results of macroeconomic dynamics observed at the beginning of 2022, the authors conclude that the trend of economic growth continued in the first quarter, and for a number of indicators in the first half of this year. However, this positive trend began to undergo significant changes. It is emphasized that the unprece- dented financial, monetary, trade, economic, informational and other sanctions imposed to Russia required the current management system to make adjustments to the principles and priorities of the state socio-economic policy.
The rationale is given for the fact that under the pressure of world geopolitics, the tasks of countering the sanctions wars declared to Russia have taken on key positions. It is concerned with providing social guarantees, ensuring the stability of the financial and monetary systems, stabilizing the consumer market, prices and inflation, as well as searching for more reliable foreign trade partners and mechanisms for set- tlements between them in national currencies.
The validity of the formation of strategic development indicators for the next three-year period 2023–2025 based on the principles and priorities of the new state socio-economic policy is noted.

The purpose of this paper is to empirically explore the potential link between the adoption of Industry 4.0 technologies in the manufacturing industry and the development of sustainable manufacturing, understood as the production of goods with the minimum use of energy and natural resources, while maintaining maximum profit and ensuring the health and safety of society throughout the product life cycle. The article first addresses 4 research questions, the first of which concerns a possible connection between the introduction of Industry 4.0 technologies and the presence of an ISO 14001 certificate in an industrial enterprise, considered as an indirect indicator of compliance with the principles of sustainable manufacturing, the second – the connection between the implementation of Industry 4.0 technologies and «green» industrial technologies, the third – the links between the introduction of Industry 4.0 technologies and the promotion of various specific areas of greening, and the fourth – the links between the introduction of digital technologies and the recognition of significant environmental benefits from the use of digital technologies in the enterprise. The analysis was based on quantified data from the annual market survey of the digital activity of Russian manufacturing enterprises for 2021, which includes a set of indicators characterizing technological and digital activity in the field of greening and increasing resource efficiency.
The obtained results indicate that, although at the technological level, the relationship between the development in the field of Industry 4.0 and the field of «green» industrial technologies is quite unambiguous, from the viewpoint of the enterprise's compliance with the criteria for sustainable production, to a lesser extent, one can speak of the important role of Industry 4.0 technologies. The presence of environmental benefits from the introduction of digital technologies was more often noted by those respondents in whose enterprises artificial intelligence and big data technologies were introduced. The same technologies were recognized as the key technologies of Industry 4.0 for sustainable development, associated with the largest number of individual areas of greening production, according to the results of the study.

The paper deals with certain aspects of the statistical study of how advanced production technologies are implemented at the present stage of scientific and technological progress in Russia. This matter is addressed from two perspectives: statistics on the development and use of advanced production technologies and statistics on stimulating the greatest possible return on the results of the introduction of advanced production technologies in the shortest period of time possible.
The author formulates proposals to improve the system of accounting indicators by improving the quality of the selection of organizations that develop and use advanced production technologies, as well as the quality of accounting for unaccounted technologies at all levels of management. Recommendations are given for adjusting each of the main areas of use of the evaluation indicators, as well as improving the methodology for the formation of the evaluation indicators themselves, in particular, by applying a score to each of them.
The statistics of advanced production technologies implementation is evaluated. Particular attention is paid to accounting for the formation of applications and their implementation in such areas as patent issuance, registration of trademarks and industrial designs. The article considers activity of the World Intellectual Property Organization (WIPO) in the area of patent statistics.
The author explains the need to gradually combine the two forms of statistical accounting – state (Rosstat) and WIPO statistics – into a single form, which will allow, at the early stages of development and use of technologies, to assess their quality and take appropriate measures to improve them.

The article presents the results of a statistical analysis of trends in the change in the number of students studying in IT specialties in Russian higher educational institutions, and also, based on the econometric methods of data analysis, characterizes universities with a high number and a significant proportion of students studying in information technology programs. The novelty of this study, according to the author, lies in the fact that the calculations are made on the basis of a large sample taking into account changes in its dynamic characteristics (information on the activities of 611 universities and 467 university branches for 2015/2016, 2017/2018 and 2019/2020 academic years was studied).
Statistical analysis showed that in Russia only a few universities specialize in training students for IT field. So, in the 2019/2020 academic year, more than 60% of students studied in IT specialties in nine higher educational institutions alone. At the same time, IT-specialists are trained in half of the universities and in a third of the country's university branches. Over the period from 2015/2016 to 2019/2020 academic year, the number of students enrolled in IT specialties has increased in Russia by 31%.
The regression analysis of the data revealed a positive relationship between the indicators of the number of students in IT specialties in universities (total number, absolute increase in the number and their share in total student body) and the following indicators: share of young professionals in the total number of faculty members; number of partner enterprises; number of technology parks and small businesses in the university; income from research and development and number of publications in Scopus. A negative relationship is observed between the number of students in IT specialties and the share of persons with academic degrees in the total number of faculty members, as well as between the share of students in IT specialties in the total number of students and the indicators of internationalization of the composition of students and teaching staff.
The proposed approach made it possible, on the basis of a representative sample of Russian higher education institutions, to assess the relationship between the indicators of the number of IT students at the university and the results of its activities in the areas considered, as well as to determine the characteristics of higher education institutions that made a significant contribution to the training of IT specialists.
The results of the study presented in the article may be of interest to the universities that plan to significantly increase the number of students in the coming years and improve the quality of admission of applicants for training in IT specialties.