Mathematical foundation

The development of high-dimensional mathematical theory of statistics was initiated by A.N.Kolmogorov in 1968. It is based on the new asymptotic approach in which sample size increases along with the dimension of observations so that their ratio tends to a constant. This approach leaves the traditional idea of a possibility of an infinite choice of data from populations, leaves the idea of consistency, and turns to construction of estimators and procedures of maximum quality. In the increasing dimension asymptotics, the leading terms of quality functions are isolated, analyzed and maximized. Some wide classes of regularized statistical procedures are considered, and their asymptotically dominating versions are constructed. As a result, the most usable methods of multivariate statistical analysis are provided with certainly non-degenerating approximately unimprovable free from distributions procedures. For low dimension, these procedures pass to traditional consistent solutions.


Owing to the absence of degeneration of new multivariate statistical procedures and their independence of distributions, the practical investigator gets free from the necessity of consultations with specialists in statistics. It means that multivariate analysis and the new statistical software becomes accessible for a substantially wider class of users. With an addition of elements of an artificial intelligence and more friendly service, new programs can be created that can be readily used by common users uneducated neither in statistics nor in programming. A problem of a reconstruction of the existing well-known packages of statistical software arises.