Elsevier Publishing House, 2008


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The progress of information technologies puts forward statistical problems that, until recently, had no mathematical solution as well as program support. This monograph presents mathematical theory extending the statistical method to a new sphere of applications different by using models with number of unknown parameters so large that it is comparable with sample size and can be much more. This theory may be called essentially multivariate or multiparametric. The monograph presents the summation of all previous author's investigations carried out in the Kolmogorov asymptotics of increasing dimension and its extension to infinite-dimensional parameter space. A series of new more powerful multiparametric solutions are proposed to such basic multivariate problems as the estimation, regression, discriminant analysis, and solution to systems of random linear equations. These solutions have obvious theoretical and practical advantages as compared with conventional multivariate statistical procedures: they are applicable to data of any dimension, are always stable and approximately unimprovable independently of distributions.


The book will be of interest for different specialists working in the development of theory and applications of mathematical statistics. Mathematicians will find new classes of urgent problems to be solved in their regions. Specialists in applied statistics creating modern statistical software will be interested in implementing new more powerful and more efficient algorithms proposed in the book. Researchers applying statistical methods for practical problems will enjoy the sense of liberation from the danger of degeneration and instability that is characteristic for existing multivariate statistical procedures and will get a tool for efficient treatment of data without restrictions on the dimension. Students and postgraduates will be interested in this book since it will help them to get at the foremost of statistical science and guarantee the success in their future carrier.
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