NEW AGE OF MULTIVARIATE STATISTICS

Mathematical foundation

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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.

### Algorithms

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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.