# Multiparameter Methods are the New Field in Statistics

## Abstract

During the last decade statistical problems of a new kind have appeared more and more often, in which the dimensionality of observations is large, and the sample size is small or comparable with the dimensionality of observations. These problems may be characterized as multiparameter problems. The theory of multiparameter analysis, proposed by A.N.Kolmogorov and supported by the studies on the spectral theory of random matrices of V. A.Marchenko, L. A.Pastur, V. L.Girko, and others, revealed some specific phenomena appearing in statistics with a large number of weakly dependent variables. Particularly, there are stable relations between the principal parts of parameter set functions and the set of observed variables, which may be used to improve the statistical analysis. The use of these phenomena allows one to develop a thorough, always stable, and approximately optimal (irrespective of samples) versions of mostly used statistical procedures. The multiparameter versions of the discriminant analysis are of special interest.

- Authors:

- Moscow Institute of Electronics and Mathematics (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771593

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 228; Journal Issue: 5; Conference: International seminar on stability problems for stochastic models, Zakopane (Poland), 31 May - 5 Jun 2009; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; FUNCTIONS; MATRICES; MULTI-PARAMETER ANALYSIS; RANDOMNESS; STATISTICS

### Citation Formats

```
Serdobolskii, V. I., E-mail: vserd@mail.ru.
```*Multiparameter Methods are the New Field in Statistics*. United States: N. p., 2018.
Web. doi:10.1007/S10958-017-3642-7.

```
Serdobolskii, V. I., E-mail: vserd@mail.ru.
```*Multiparameter Methods are the New Field in Statistics*. United States. doi:10.1007/S10958-017-3642-7.

```
Serdobolskii, V. I., E-mail: vserd@mail.ru. Thu .
"Multiparameter Methods are the New Field in Statistics". United States. doi:10.1007/S10958-017-3642-7.
```

```
@article{osti_22771593,
```

title = {Multiparameter Methods are the New Field in Statistics},

author = {Serdobolskii, V. I., E-mail: vserd@mail.ru},

abstractNote = {During the last decade statistical problems of a new kind have appeared more and more often, in which the dimensionality of observations is large, and the sample size is small or comparable with the dimensionality of observations. These problems may be characterized as multiparameter problems. The theory of multiparameter analysis, proposed by A.N.Kolmogorov and supported by the studies on the spectral theory of random matrices of V. A.Marchenko, L. A.Pastur, V. L.Girko, and others, revealed some specific phenomena appearing in statistics with a large number of weakly dependent variables. Particularly, there are stable relations between the principal parts of parameter set functions and the set of observed variables, which may be used to improve the statistical analysis. The use of these phenomena allows one to develop a thorough, always stable, and approximately optimal (irrespective of samples) versions of mostly used statistical procedures. The multiparameter versions of the discriminant analysis are of special interest.},

doi = {10.1007/S10958-017-3642-7},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 5,

volume = 228,

place = {United States},

year = {2018},

month = {2}

}