Center for General Statistical Analysis and Theory of Random Operators

Directed by Prof. Vyacheslav L. Girko

Vyacheslav Girko


Prof. Girko's new book will soon be available on this web page!

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Introduction

The Center for General Statistical Analysis was founded by Prof. Vyacheslav L. Girko in January 2000.

The goals of the center are:

  1. Further development of General Statistical Analysis and relevant sciences.
  2. Publication of journals.
  3. Publication of books and proceedings.
  4. Organization of conferences and symposiums.
  5. Organization of seminars and courses for students and professors to further study GSA.
  6. Solving practical problems.

Contact information

Institute of Mathematics
Ukrainian National Academy of Sciences


Tereshchenkivska
3,
01601, Kiev-4, Ukraine

E-mail:agirko@i.com.ua

Curriculum Vitae


Prof. Girko is editor of the following journals

Random Operators and Stochastic Equations (ROSE)

Statistical Analisis of Random Arrays (SARA) (in preparation)


Staff and Editorial Board

L. Accardi (Rome)

S. Albeverio (Bochum)

G. Cassati (Como)

V. Kurotschka(Berlin)

Y. Kondratyev (Bielefeld)

I. Litvin(Port Elizabeth)

H. Drygas (Kassel)

N. Portenko (Kiev)

N. Leonenko(Kardiff)

A. Vladimirova (Kiev)

A. F. Turbin (Kiev)

I. Ibragimov (St. Petersburg)

Yuri Krak (Kiev)

S. Molchanov (Charlotte, NC)

W. Kirsch (Bochum)

N. Christopeit (Bonn)

L. Pastur (Marsel)

A. Klein (Irvine, CA)

A. Shiryayev (Moscow)

M. B. Malyutov (Boston)

C. Domanski (Lodz)

A. Rukhin (Baltimore)

V. Fedorov (Tennessee)

Muni S. Srivastava (Canada)

E. Staffetti (Rome)

E. Lebedev (Kiev)

A. Babanin (Kiev)

A. Nakonechny (Kiev)

Ph. Loubaton (Marne-la-Vallee)

R. Carmona (Princeton)


Books

 

 

 

Theory of Stochastic Canonical equations, Kluwer Academic Publishers, The Netherlands, 2001

An Introduction to Statistical Analysis of Random Arrays. VSP, The Netherlands, 1998

Multidimensional Statistical Analysis and Theory of Random Matrices. VSP, The Netherlands, 1996

Theory of Linear Algebraic Equations With Random Coefficients. Allerton Press, Inc, New York, USA, 1996

Statistical analysis of observations of increasing dimension. Kluwer Academic Publishers, The Netherlands, 1995

Theory of Random Determinants Kluwer Academic Publishers, The Netherlands, 1990

Theory of Systems of Empirical Equations. "Lybid Publishing, Kiev, Ukraine, 1990

Spectral Theory of Random Matrices. "Science" Publishing, Moscow, Russia, 1988

Multidimensional Statistical Analysis. "Higher School" Publishing, Kiev, Ukraine, 1983

Limit Theorems for Functions of Random Variables. "Higher School" Publishing, Kiev, Ukraine, 1983

Theory of Random Determinants. Kiev University Publishing, Ukraine, 1975

Random Matrices. Kiev University Publishing, Ukraine, 1975

Candidate of Science Thesis, Kiev University, Ukraine, 1972


Recent Papers

 

The Canonical Equation for the Resolvent of a Random Matrix with Asymptotically Independent Entries II. Random Operators and Stochastic Equations, V. 3, N.1, 1995, 41--63 p.

The Method of Random Determinants for Estimating the Permanent. Random Operators and Stochastic Equations, V. 3, N.2, 1995, 181--193 p.

Canonical Spectral Equation for the Empirical Covariance Matrices, Ukrainian Mathematical Journal , 1995, V. 47, N.9, 1176--1189 p.

Elliptic Law: Ten Years Later I, Random Operators and Stochastic Equations, V. 3, N. 3, 1995, 257--302 p.

The Elliptic Law: Ten Years Later II, Random Operators and Stochastic Equations}, V. 3, N.4, 1995, 377--398 p.

Random Matrices, Handbook of Algebra. Elsevier Science B.V. 1995, 27--78 p.

Canonical Equation for Empirical Covariance Matrices. Proceedings of the 14-th International Conference on Multivariate Statistical Analysis, MSA95, Warsaw, Poland, 1995, 225--247 p.

Minimax Estimators for Linear Models with Nonrandom Disturbances. Random Operators and Stochastic Equations V. 3, N.4, 1995, 361--377 p. (with N. Christopeit).

Spectral Theory of Minimax Estimation, Acta Applicandae Mathematicae V.3, 1996, 59--69 p.

The Canonical Spectral Equation, Theory of Probability and its Applications, V. 39, N.4, 1996, 685--691 p.

Canonical Equation for the Resolvent of Empirical Covariance Matrix, Random Operators and Stochastic Equations, V.4, N.1, 1996, 61--76 p.

Strong Law for the Eigenvalues and Eigenvectors of Empirical Covariance Matrices, Random Operators and Stochastic Equations, V.4, N.2, 1996, 179--204 p.

Multivariate Elliptically Contoured Linear Models and Some Aspects of the Theory of Random Matrices, "Multidimensional Statistical Analysis and Theory of Random Matrices". Proceedings of the Sixth Eugene Lukacs Symposium Held in Bowling Green State University, Department of Mathematics and Statistics, Bowling Green Ohio. Publishing VSP (with A.K. Gupta) 1996, 327--387 p.

Canonical equation for the resolvent of empirical covariance matrices pencil, "Multidimensional Statistical Analysis and Theory of Random Matrices". Proceedings of the Sixth Eugene Lukacs Symposium Held in Bowling Green State University, Department of Mathematics and Statistics, Bowling Green Ohio. Publishing VSP. (with A.K. Gupta), 1996, 41--61 p.

Strong Law for the eigenvalues of empirical covariance matrices. "Multidimensional Statistical Analysis and Theory of Random Matrices". Proceedings of the Sixth Eugene Lukacs Symposium Held in Bowling Green State University, Department of Mathematics and Statistics, Bowling Green Ohio. Publishing VSP. 1996, 61--92 p.

Distribution of spacings of random matrices. Part I: The First Spacing Law for Gaussian Hermitian matrices, Random Operators and Stochastic Equations V.4, N.3, 1996, 283--300 p.

Numerical and Monte Carlo Verification of the First Spacing Law, Random Operators and Stochastic Equations. V.4, N.4, 1996, 303--314 p. (with N. Preston).

A matrix equation for the resolvents of random matrices with independent blocks. Theory of Probability and its Applications, V.40, 4, 635--644 (1996).

Limit theorems for permanents. Theory of Probability and mathematical statistics, No. 53, 33--42 (1996).

Strong Law for the singular values and eigenvectors of random matrices, I. Random Operators and Stochastic Equations, V.5, N.1, 1997, 80--104.

Strong Circular Law. Random Operators and Stochastic Equations, V.5, N.2, 1997, 173--197.

Strong Elliptic Law. Random Operators and Stochastic Equations, V.5, N.3, 1997, 269--306.

The $V$-density for eigenvalues of non symmetric random matrices and rigorous proof of the strong Circular law, Random Operators and Stochastic Equations, V.5, N.4, 371--406 (1997).

A Refinement of the central limit theorem for random determinants, Theory of Probability and Its Applications, V.42, N.1, 121--129 (1997).

Numerical and Monte -Carlo Verification of the $V$-Law, Random Operators and Stochastic Equations, V.6, N.2, 1998, 80--104. (with R. Dias)

Strong Law for the singular values and eigenvectors of random matrices II. Random Operators and Stochastic Equations, V.6, N.3, 1998, 291--310.

Convergence rate of the expected spectral functions of symmetric random matrices equals $O(n^{-1/2})$. Random Operators and Stochastic Equations, V.6, N.4, 1998, 359--406.

The $V$-relation between Hermitian and Non-Hermitian Operators and Strong Law for Normalized Spectral Functions of Non-Selfadjoint Random Matrices with Independent Row Vectors. Markov Processes and Related Fields V.4, 4, 499--508 (1998).

Strong Law for the singular values and eigenvectors of random matrices III. Inequalities for the spectral radius of large random matrices, Random Operators and Stochastic Equations, V.7, N.2, 1999, 179--200.


Simulation of Eigenvalues of Random Matrices

 

Numerical and Monte Carlo verification of V-distribution


Scientific Projects

Proposition of a theory of optimization for obtaining minimax estimators of the parameters of the regression models

The Development of Statistical Analysis of Random Arrays and Its Programm Applications


The Main Law of the Theory of Random Matrices

Wigneręs Semicircle Law

Circular Law

Inverse Tangent Law

The Logarithmic Law

Strong Elliptic Law

Elliptic Law

Ten Spacings Laws

The Second Law for the Singular Values and Eigenvectors of Random Matrices

The Third Law for the Eigenvalues and Eigenvectors of Empirical Covariance Matrices

The Law of Large Numbers for the Product of Independent Random Matrices

The Central Limit Theorem for the Product of Independent Random Matrices

The Central Limit Theorem for the Resolvents of Random Matrices

Strong V-Law

Uniform V-Law


The Main Minimax Estimators

Spectral Equation S1 for Minimax Estimators of Parameters in Linear Models

Linear Models with Unknown Covariance Matrix -- Spectral Equation S2

Linear Models with Nonrandom Perturbations -- Spectral Equation S3

Spectral Equation S4 for the Estimators of the Solutions of Systems of Equations with "Internal" Perturbations in System of Observations

Linear Models with an Arbitrary Set of Perturbations -- Spectral Equation S5

ESTIMATION of States of Some Recursively Defined Systems -- Spectral Equation S6

Estimation of States of Some Systems Which Are Described by Recursive Equations -- Spectral Equation S7


The Main Estimators of GSA

G1-Estimator of Generalized Variance

G2-Estimator of Real Stieltjes Transform of the Normalized Spectral Function of Covariance Matrices

G3-Estimator of Inverse Covariance Matrix

Class of G4-Estimators for the Traces of the Powers of Covariance Matrices

G5-Estimator of Smoothed Normalized Spectral Function of Symmetric Matrices

G6-Estimator of Stieltjes' Transform of Covariance Matrix Pencil

G7-Estimator of the States of Discrete Control Systems

Class of G8-Estimators of the Solutions of Systems of Linear Algebraic Equations (SLAE)

G9-Estimator of the Solution of the Discrete Kolmogorov-Wiener Filter

G10-Estimator of the Solution of a Regularized Discrete Kolmogorov-Wiener Filter With Known Free Vector

G11-Estimator of the Mahalanobis Distance

G12-Regularized Mahalanobis Distance Estimator

G13-Discrimination of Two Populations With Common Unknown Covariance Matrix. G13-Anderson-Fisher Statistics Estimator

G14-Estimator of Regularized Discriminat Function

G15-Estimator of the Nonlinear Discriminant Function, Obtaind by Observation of Random Vectors With Different Covariance Matrices

G16-Class of G1-Estimators in the Theory of Experimental Desgn, When the Design Matrix is Unknown

G17-Estimate of T2-Statistics

G18-Estimate of Regularized T2-Statistics

Quasi-Inversion Method for Solving $G$-Equations

Estimator $G {20}$ of Regularized Function of Unknown Parameters

G21-Estimator: Estimator in the Likelihood Method

 


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