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## Статистический анализ моделей с переменной структурой

Classification problems for univariate and multivariate observations are often encountered in statistics and economics. However, all existing approaches to solving these problems have several essential drawbacks:

1. All these methods cannot help in testing the null hypothesis of no different classes;

2. The number of classes is assumed to be known a priori;

3. Theoretical justification of performance effectiveness of these methods is lacking.

In this paper a new nonparametric method is proposed which can help us to solve these problems. This method enables us to construct consistent estimate of an unknown number of classes and to test the null hypothesis of no different classes. Besides theoretical findings, we present results of experimental analysis of this method including comparison of its characteristics with the maximum likelihood method and k-means method in different situations.

The contemporary marketing practices methodology (CMP) attracts attention of a substantial number of researchers in the field of strategic marketing. In the past two decades there were more than fifty papers published in peer-reviewed outlets addressing the analytics of usage of contemporary marketing practices in a variety of countries and industries. In this note we discuss reliability of these studies with respect to the usage of specific analytic tools. First, we demonstrate that standard clustering analysis is relatively sensitive to small changes in the datasets with companies being assigned to different clusters at frequent rates. Second, the project national teams make use of different, often incompatible settings. Therefore, to make possible comparisons between the countries and across industries, the researchers must agree on a generic setup and procedures. We conclude the note sketching the basics of these common grounds.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

The main goal of this paper is to study interconnections between credit ratings and financial indicators of industrial companies from BRICS countries. We use method of patterns, one of the modern methods of nonlinear modeling, to identify groups of heterogeneous objects with different influence on ratings. Additionally, in this research, we evaluate Tobit regression model for selected groups and establish some credit rating patterns for the BRICS industrial companies. Our results of Tobin model, may have practical implementation in short-term financial management.

The main goal of this paper is to study interconnections between credit ratings and financial indicators of industrial companies from BRICS countries. We use method of patterns, one of the modern methods of nonlinear modeling, to identify groups of heterogeneous objects with different influence on ratings. Additionally, in this research, we evaluate Tobit regression model for selected groups and establish some credit rating patterns for the BRICS industrial companies. Our results of Tobin model, may have practical implementation in short-term financial management.

Data Mining in Agriculture represents a comprehensive effort to provide graduate students and researchers with an analytical text on data mining techniques applied to agriculture and environmental related fields. This book presents both theoretical and practical insights with a focus on presenting the context of each data mining technique rather intuitively with ample concrete examples represented graphically and with algorithms written in MATLAB®.

This book concentrates on in-depth explanation of a few methods to address core issues, rather than presentation of a multitude of methods that are popular among the scientists. An added value of this edition is that I am trying to address two features of the brave new world that materialized after the first edition was written in 2010. These features are the emergence of “Data science” and changes in student cognitive skills in the process of global digitalization. The birth of Data science gives me more opportunities in delineating the field of data analysis. An overwhelming majority of both theoreticians and practition-ers are inclined to consider the notions of ‘data analysis” (DA) and “machine learning” (ML) as synonymous. There are, however, at least two differences between the two. First comes the difference in perspectives. ML is to equip computers with methods and rules to see through regularities of the environment - and behave accordingly. DA is to enhance conceptual understanding. These goals are not inconsistent indeed, which explains a huge overlap between DA and ML. However, there are situations in which these perspectives are not consistent. Regarding the current students’ cognitive habits, I came to the conclusion that they prefer to immediately get into the “thick of it”. Therefore, I streamlined the presentation of multidimensional methods. These methods are now organized in four Chapters, one of which presents correlation learning (Chapter 3). Three other Chapters present summarization methods both quantitative (Chapter 2) and categorical (Chapters 4 and 5). Chapter 4 relates to finding and characterizing partitions by using K-means clustering and its extensions. Chapter 5 relates to hierarchical and separative cluster structures. Using encoder-decoder data recovery approach brings forth a number of mathematically proven interrelations between methods that are used for addressing such practical issues as the analysis of mixed scale data, data standardization, the number of clusters, cluster interpretation, etc. An obvious bias towards summarization against correlation can be explained, first, by the fact that most texts in the field are biased in the opposite direction, and, second, by my personal preferences. Categorical summarization, that is, clustering is considered not just a method of DA but rather a model of classification as a concept in knowledge engineering. Also, in this edition, I somewhat relaxed the “presentation/formulation/computation” narrative struc-ture, which was omnipresent in the first edition, to be able do things in one go. Chapter 1 presents the author’s view on the DA mainstream, or core, as well as on a few Data science issues in general. Specifically, I bring forward novel material on the role of DA, including its successes and pitfalls (Section 1.4), and classification as a special form of knowledge (Section 1.5). Overall, my goal is to show the reader that Data science is not a well-formed part of knowledge yet but rather a piece of science-in-the-making.

This paper presents a clustering algorithm, namely MFWK-Means, which is a novel extension of K-Means clustering to the case of fuzzy clusters and weighted features. First, the Weighted K-Means criterion utilizing Minkowski metric is adopted to solve the problem of feature selection for high dimensional data. Then, a further extension to the case of fuzzy clustering is presented to group datasets with natural fuzziness of cluster boundaries. Also, we adopt an intelligent version of K-Means, using Mirkin’s method of Anomalous Pattern for initialization. Our new Minkowski metric Fuzzy Weighted K-Means (MFWK-Means) is experimentally validated on both benchmark datasets and synthetic datasets. MFWK-Means is shown to be competitive and more stable against noise in comparison with a variety of versions of K-Means based methods. Moreover, in most situations it reaches the highest clustering accuracy at wider intervals of Minkowski exponent.

Authors suggests some advices in the field of client base segmentation construction for retail profit-making organizations concerning their possible reaction on marketing campaigns. Advices are based on the results of research in one of the largest Russian retail network in the segment of mobile devices.

A brief overview of the results of the classification of the RF-regions by the distributions of the EGE-scores in 2011 year is presented. The comparison analysis of these results with the results in 2010 year is made. The attempt to establish the factors that explain the variation of the region's distributions is made. The multiple linear regression for the average score under these factors is build.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.