The reason for the research is Russia's transition to the model of sustainable development. The environmental component plays the important role in the formation of sustainable development of the territories. This research area enables to estimate the influence of environmental parameters on the level of sustainable development of territories. Indicators characterizing the state of the environment and ecological potential of these territories were used as indicators which have an impact on sustainable development. This research was carried out on the basis of multiple regressions method. For the first time the classification of regions of the Russian Federation for 2013 by the level of environmental safety was made. As a result, the most significant indicators affecting the sustainable development of territories were revealed and decisions for the management of these parameters were developed in order to improve the sustainable development of territories.

The ecology becomes a limiting factor for the sustainable development of the country in general, as well as its certain regions. The issue of assessment of the level of ecological safety of territories arises.The article considers the assessment technique of the composite index of Environmental Safety by aggregation of three indicators reflecting social and economic development, ecological conditions and human capacity of the region. The aggregation is offered to be carried out by means of the method of multivariate average. Official data of the Federal State Statistics Service is used for the calculation of indicators. Original aggregate is divided into two or three groups by each indicator and composite index of environmental safety of the region. It makes it possible to define a place of the region in space of indicators, to identify type of the studied territory by the level of environmental safety and to develop effective strategies of ecological safety management both for a separate territorial unit and for homogeneous groups.The suggested methodology makes it possible to obtain rather adequate estimates for main territorial levels of management – municipal, subjective, district

The Jarque–Bera test is commonly used in statistics and econometrics to test the hypothesis that sample elements adhere to a normal distribution with an unknown mean and variance. This paper proposes several modifications to this test, allowing for testing hypotheses that the considered sample comes from: a normal distribution with a known mean (variance unknown); a normal distribution with a known variance (mean unknown); a normal distribution with a known mean and variance. For given significance levels, $\alpha =0.05$ and $\alpha =0.01$, we compare the power of our normality test with the most well-known and popular tests using the Monte Carlo method: Kolmogorov–Smirnov (KS), Anderson–Darling (AD), Cramér–von Mises (CVM), Lilliefors (LF), and Shapiro–Wilk (SW) tests. Under the specific distributions, 1000 datasets were generated with the sample sizes $n=25,50,75,100,150,200,250,500,$ and 1000. The simulation study showed that the suggested tests often have the best power properties. Our study also has a methodological nature, providing detailed proofs accessible to undergraduate students in statistics and probability, unlike the works of Jarque and Bera.

The article focuses on the problem of assessing the level of the fuzzy phenomena as environmental safety territorial entities. The study presents a solution to this problem by neural networks. Application of neural networks allows to overcome the lack of available information on the input and to carry out the correct assessment of the environmental safety of territorial entities. Method of training a neural network is used for this. The advantages of using fuzzy neural networks are the flexibility and the opportunity to work directly with implicit parameters and criteria known to approximate or unknown data; a tolerance of ambiguities and contradictions of used data. This technique allowed solve the following tasks: to carry out a typology of subjects of the Russia in terms of environmental safety and to develop scenarios increase their security; to perform a forecast of changes in their development, taking into account environmental factors