Scientific Journal of KubSAU

Some estimators of the probability density function in spaces of arbitrary nature are used for various tasks in statistics of non-numerical data. Systematic exposition of the theory of such estimators had a start in our work [2]. This article is a direct continuation of the article [2]. We will regularly use references to conditions and theorems of the article [2], in which we introduced several types of nonparametric estimators of the probability density. We studied more linear estimators. In this article we consider particular cases - kernel density estimates in spaces of arbitrary nature. When estimating the density of the one-dimensional random variable, kernel estimators become the Parzen-Rosenblatt estimators. Asymptotic behavior of kernel density estimators in the general case of an arbitrary nature spaces are devoted to Theorem 1 - 8. Under different conditions we prove the consistency and asymptotic normality of kernel density estimators. We have studied uniform convergence. We have introduced the concept of "preferred rate differences" and studied nuclear density estimators based on it. We have also introduced and studied natural affinity measures which are used in the analysis of the asymptotic behavior of kernel density estimators. We have found the asymptotic behavior of dispersions of kernel density estimators and considered the examples including kernel density estimators in finite-dimensional spaces and in the space of square-integrable functions

According 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

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

Improvement of the organizational structures can increase the efficiency of enterprises. Controlling of personnel in companies such as "Research Institute" is a tool to support personnel decisions; it contributes to the strategic goals and tactical objectives. This article describes the main types of organizational structures, their properties, sociometric research as a tool for management, the stages of implementation of model of controlling of personnel in human resource management system for companies such as "Research Institute". Controlling of personnel is in regulation of HR processes, benchmarking, monitoring the implementation of the goals, taking into account the costs of implementing improved management systems, etc. It aims to determine the quality, efficiency and optimality of specific mechanisms, technologies and methods for the implementation of the HR function. Objectively, the volume of realization of the HR function depends on the presence of a certain quantities of material, labor, financial and other resources, on the objectives of the enterprise at different stages of the life cycle, as well as the number and qualifications of personnel. The quality of realization of the HR function depends on the level of its top-management's understanding of the importance of human resource management in the enterprise, as well as of the skill level of middle management. Controlling of HR function allows us to create an information base for effective management decisions that can help us to optimize the system of personnel management in the circumstances of the market environment, which is a necessary basis for the successful development of enterprises working in the field of high technology products and services

Currently, the majority of scientific, technical and economic studies use statistical methods developed mainly in the first third of the XX century. They constitute the content of common textbooks. However, mathematical statistics are rapidly developing in the next 60 years. In some situations there is a need of the transition from classical to modern methods. As an example, we discuss the problem of testing the homogeneity of two independent samples. We have considered the conditions of applicability of the traditional method of testing the homogeneity based on the use of Student's t-statistic, as well as more up-to-date methods. We describe a probabilistic model of generation of statistical data in the problem of testing the homogeneity of two independent samples. In terms of this model the concept of "homogeneity" ("no difference"), can be formalized in different ways. High degree of homogeneity is achieved if the two samples are taken from one and the same population (absolute homogeneity). In some cases it is advisable to testing the coincidence of some characteristics of the elements of the sample - mathematical expectations, medians, variances, coefficients of variation, and others (testing the homogeneity of characteristics). To test the homogeneity of mathematical expectations is often recommended classic t-test. It is believed that the samples taken from a normal distributions with equal variances. It is shown that for scientific, technical and economic data the preconditions of two-sample t-test usually are not performed. To test the homogeneity of mathematical expectations instead of t-test we have offered to use the Cramer-Welch test. We have considered the consistent nonparametric Smirnov and Lehmann-Rosenblatt tests for absolute homogeneity

The mathematical theory of classification contains a large number of approaches, models, methods, algorithms. This theory is very diverse. We distinguish three basic results in it - the best method of diagnosis (discriminant analysis), an adequate indicator of the quality of discriminant analysis algorithm, the statement about stopping after a finite number of steps iterative algorithms of cluster analysis. Namely, on the basis of Neyman - Pearson Lemma we have shown that the optimal method of diagnosis exists and can be expressed through probability densities corresponding to the classes. If the densities are unknown, one should use non-parametric estimators of training samples. Often, we use the quality indicator of diagnostic algorithm as "the probability (or share) the correct classification (diagnosis)" - the more the figure is the better algorithm is. It is shown that widespread use of this indicator is unreasonable, and we have offered the other - "predictive power", obtained by the conversion in the model of linear discriminant analysis. A stop after a finite number of steps of iterative algorithms of cluster analysis method is demonstrated by the example of k-means. In our opinion, these results are fundamental to the theory of classification and every specialist should be familiar with them for developing and applying the theory of classification

When considering the ecological safety of industrial productions, territory, etc., we usually allocate the constant (permanent) risk and the accident (emergency) risk. Permanent risk is given by the used technology, and cannot be changed substantially. Emergency risks are associated with uncertainty, in contrast to the constant risks. Let in adopted mathematical model the uncertainty is probabilistic in nature, and the loss describes as one-dimensional random variable. The distribution function of the loss, as a rule, is not normal. We have discussed in detail the seven characteristics of accidental loss: expectation; median and, more generally, quantile; dispersion; standard deviation; coefficient of variation; a linear combination of the expectation and standard deviation; the expectation of the loss function. Risk management may be to minimize these characteristics and their combinations (in different variants of multicriteria optimization). For example, in the two-criteria formulation it is required to minimize the expectation of loss and the standard deviation. Two-criteria formulation one way or another is reduced to a one-criteria formulation. In addition to probabilistic methods of risk modeling, sometimes we consider methods for describing risk using by means of objects of non-numeric nature, in particular qualitative characteristics, concepts of the theory of fuzzy sets, interval mathematical and econometric models and other mathematical tools. The main problems of the theory and practice of ecological insurance have been discussed

Controlling of statistical methods to ensure product quality is the special case of controlling organizational and economic methods of management. Today, controlling in the practice of management of Russian companies is understood as "the system of information-analytical and methodological support to achieve their goals." The controller is developing a decision-making rules, the head takes decisions on the basis of these rules. We proved the concept of "controlling of methods". Innovation in management is based, in particular, on the use of new adequate organizational-economic (as well as economicmathematical and statistical) methods. Controlling in this area - is the development and application procedures of compliance management used and newly developed (implemented) organizationaleconomic methods for the task. Thus, the methodology for controlling is of great practical value in any field in which the actions (operations) must be carried out in accordance with certain rules (regulations, standards, guidelines), as in any such area in which we need to use development and application procedures of compliance management used and the newly established (implemented) rules for solution of tasks assigned to the organization. In this article, we select a area of controlling as controlling quality, and we discuss its main issues. This is about controlling of organizational-economic methods to ensure product quality, especially about the statistical methods based on probability theory and mathematical statistics. We consider the analysis and synthesis of plans of statistical quality control, optimization options plans of statistical control, truncated plans. Are discussed the differences control plans provider and the consumer, the allocation of units formless (liquid, gas) products, the selection of a random sample of the statistical quality control of products, lower estimate of the required sample size. It is established, that is not always necessary quality control. Is given the theory of the basic paradox of statistical quality control. We discuss the development of statistical methods for quality control in our country. Is given the classification of statistical methods of quality management

In many areas - the economy, quality management, medicine, the ecology, in safety of flights and others - the problems of analysis, estimation and management of risks have much in common. Therefore, we consider it necessary to develop a general theory of risk. Approaches and methods of this theory will allow in the future solving problems of uniform risk management in specific subject areas. Based on the analysis of scientific publications and industry regulations it must be noted that private risk theories tend to become isolated within themselves, create their own internal standards and systems of regulations. Separately - for banking, separately - for safety, separately - for industrial accidents, etc. In order to construct a general theory of risk we analyze use of the term "risk" in various fields, consider the variety of types of risks, give the basic definitions in the field of analysis, estimation and management of risk. We discuss planetary risks (at Earth as a whole), global risks (at the level of one or more States), financial risks, commercial risks (risks at the level of the immediate environment of the company), and production (internal, operational) risks relating to the activities of individual enterprises (organizations), personal risks. Instruments of total risk theory allow us equally solve the basic problems of analysis, estimation and management of risk for all areas

Of the many urgent problems of Science about Science, we consider methods for estimation of the effectiveness and quality of the scientific activities of the researcher, of the organization, of the magazine. Performance indicators of scientific activity are used as an important part in the estimation of higher education institutions, the innovative capacity of enterprises, etc. To estimate the effectiveness of scientific activity is natural to use intellectual tools which are well-established in other subject areas. This will include, in particular, the balanced scorecard, based on key performance indicators (hence the title of this article), as well as controlling, primarily controlling of research activities. There are two more developed and widely used tools for estimation the effectiveness of the scientific activity - the scientometric indicators and the expert estimators. Their critical analysis is the subject of this article. Different versions of manipulating of values of scientometric indicators in the Russian Federation, in our estimation, are still relatively rare. Perhaps this is due to the relatively short period of their use in the management of science. Since an indicator such as citation index (the number of citations of publications) of researcher, allows estimating its contribution to science, the use of this scientometric indicator for the management of science is justified. At the same time, the number of publications and especially h-index is not possible to objectively estimate the effectiveness of research activities, particularly in view of the properties of the real bibliometric databases. Expert procedures have several disadvantages. In this article we discuss the real effectiveness of expert procedures in the areas of their application, as conferring academic degrees and elections to the National Academy of Sciences (primarily in the Russian Academy of Sciences). The basic principles of expertise in these areas remain the same for the past 70 years. Based on an analysis of practice it is necessary to ascertain the lack of efficacy of expert estimators in these areas. Rationale to what has been said is given in the article