Statistical analysis of observations of increasing dimension:
Statistical Analysis of Observations of Increasing Dimension is devoted to the investigation of the limit distribution of the empirical generalized variance, covariance matrices, their eigenvalues and solutions of the system of linear algebraic equations with random coefficients, which are an import...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer
1995
|
| Schriftenreihe: | [Theory and decision library / B]
28 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | Statistical Analysis of Observations of Increasing Dimension is devoted to the investigation of the limit distribution of the empirical generalized variance, covariance matrices, their eigenvalues and solutions of the system of linear algebraic equations with random coefficients, which are an important function of observations in multidimensional statistical analysis. A general statistical analysis is developed in which observed random vectors may not have density and their components have an arbitrary dependence structure. The methods of this theory have very important advantages in comparison with existing methods of statistical processing. The results have applications in nuclear and statistical physics, multivariate statistical analysis in the theory of the stability of solutions of stochastic differential equations, in control theory of linear stochastic systems, in linear stochastic programming, in the theory of experiment planning. |
| Beschreibung: | Aus d. Russ. übers. |
| Beschreibung: | XXI, 286 S. |
Internformat
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Datensatz im Suchindex
| _version_ | 1804124780571394048 |
|---|---|
| adam_text | STATISTICAL ANALYSIS OF OBSERVATIONS OF INCREASING DIMENSION BY
VYACHESLAV L. GIRKO DEPARTMENT OF APPLIED STATISTICS, KIEV NATIONAL
STATE UNIVERSITY, UKRAINE * !** KLUWER ACADEMIC PUBLISHERS DORDRECHT/
BOSTON / LONDON CONTENTS CONTENTS LIST OF BASIC NOTATIONS AND
ASSUMPTIONS IX INTRODUCTION TO THE ENGLISH EDITION XI CHAPTER 1.
INTRODUCTION TO GENERAL STATISTICAL ANALYSIS 1 1. NINE CLASSES OF THE G
-SAMPLE OF OBSERVATIONS OF INCREASING DIMENSION 2 2. DISTRIBUTION
DENSITY OF THE EMPIRICAL COVARIANCE MATRIX 6 3. DISTRIBUTION OF
EIGENVALUES AND EIGENVECTORS OF THE EMPIRICAL COVARIANCE MATRIX 14 4.
G-EQUATIONS FOR ESTIMATES OF THRICE DIFFERENTIABLE FUNCTIONS OF UNKNOWN
PARAMETERS 24 5. G-EQUATION OF HIGHER ORDERS 27 6. G-EQUATION FOR
FUNCTIONS OF THE EMPIRICAL VECTOR OF EXPECTATIONS AND THE COVARIANCE
MATRIX 29 7. G-EQUATION FOR FUNCTIONS OF EMPIRICAL MATHEMATICAL
EXPECTATIONS 30 CHAPTER 2. LIMIT THEOREMS FOR THE EMPIRICAL GENERALIZED
VARIANCE 32 1. LIMIT THEOREM FOR THE SUM OF MARTINGALE-DIFFERENCES 32 2.
THE CENTRAL LIMIT THEOREM FOR GENERALIZED VARIANCE 34 3. THE METHOD OF
ORTHOGONAL TRANSFORMATIONS 39 4. THE THEOREM OF THE TYPE OF LARGE
NUMBERS LAW AND THE CENTRAL VI CONTENTS LIMIT THEOREM FOR THE EMPIRICAL
GENERALIZED VARIANCE FOR THE G 7 AND G G SAMPLES 43 5. METHOD OF NORMAL
REGULARIZATION FOR THE EMPIRICAL GENERALIZED VARIANCE 48 6. CENTRAL
LIMIT THEOREM FOR EMPIRICAL GENERALIZED VARIANCE 54 7. THE G -ESTIMATOR
OF GENERALIZED VARIANCE 57 CHAPTER 3. THE CANONICAL EQUATIONS CJ,---, C
3 FOR THE EMPIRICAL COVARIANCE MATRIX 58 1. STIELTJES TRANSFORMS, THEIR
INVERSE FORMULAS AND LIMIT THEOREMS OF A GENERAL TYPE FOR SPECTRAL
FUNCTIONS 58 2. CANONICAL EQUATION CJ FOR THE G 5 SAMPLE 61 3. INVARIANT
PRINCIPLE FOR EMPIRICAL COVARIANCE MATRICES 63 4. LIMIT THEOREM FOR
NORMALIZED SPECTRAL FUNCTIONS OF EMPIRICAL COVARIANCE MATRICES UNDER
LINDEBERG S CONDITION 66 5. DISTRIBUTION DENSITY FOR NORMALIZED SPECTRAL
FUNCTIONS WHEN COVARIANCE MATRIX HAS TWO MULTIPLY EIGENVALUES 78 6.
ASYMPTOTIC BEHAVIOR OF NORMALIZED SPECTRAL FUNCTIONS OF COVARIANCE
MATRICES FOR THE G 4 SAMPLE. CANONICAL EQUATION C 2 81 7. CANONICAL
EQUATION C 3 FOR EMPIRICAL COVARIANCE MATRICES FOR THE G 6 SAMPLE 98
CHAPTER 4. LIMIT THEOREMS FOR THE EIGENVALUES OF EMPIRICAL COVARIANCE
MATRICES 122 1. CANONICAL EQUATION CJ AND EQUATION L FOR THE EXTREME
POINTS OF SPECTRAL DENSITY 123 CONTENTS VII 2. LIMIT THEOREM FOR
NORMALIZED SPECTRAL FUNCTIONS 126 3. THE REFORM METHOD OF DERIVING THE
MAIN EQUATION OF THE SPECTRAL THEORY OF EMPIRICAL COVARIANCE MATRIX 128
4. INEQUALITIES FOR THE COEFFICIENTS OF THE MAIN EQUATION 130 5.
CALCULATIONS OF COEFFICIENTS OF THE MAIN EQUATION 135 6. INVARIANT
PRINCIPLE FOR THE EMPIRICAL COVARIANCE MATRIX 139 7. SUBSTITUTION OF THE
VECTOR OF EMPIRICAL EXPECTATION BY A NON- RANDOM VECTOR 146 8. EQUATION
FOR THE SUM OF SMOOTHED DISTRIBUTION FUNCTIONS OF EIGENVALUES OF
EMPIRICAL COVARIANCE MATRICES 157 9. FOURIER METHOD AND INVERSE FOURIER
TRANSFORM FOR FINDING THE BOUNDARIES OF EIGENVALUES 158 10. RANDOM
PERTURBATIONS METHOD FOR EIGENVALUES 164 11. THE MAIN ASSERTION 167
CHAPTER 5. G2-ESTIMATOR FOR THE STIELTJES TRANSFORM OF THE NORMALIZED
SPECTRAL FUNCTION OF COVARIANCE MATRICES 171 1. THE MAIN EQUATION OF
GENERAL STATISTICAL ANALYSIS AND G2 -ESTIMATOR 172 2. THE MAIN FORMULAS
OF REFORM METHOD 178 3. SELF-AVERAGING OF THE STIELTJES TRANSFORMS AND
INVARIANCE PRINCIPLE FOR EMPIRICAL COVARIANCE MATRICES 179 4. THE
CANONICAL SPECTRAL EQUATION 184 5. SELF-AVERAGING OF THE SOLUTION OF THE
MAIN EQUATION 186 6. THE FIRST CONSTANT OF THE G2 -ESTIMATOR 188 7. THE
SECOND CONSTANT OF THE G2 -ESTIMATOR 194 8. THE CENTRAL LIMIT THEOREM
FOR STIELTJES TRANSFORMS 199 VIII CONTENTS 9. THE SUBSTITUTION OF THE
VECTOR OF EMPIRICAL EXPECTATION BY A NONRANDOM VECTOR 203 10. ASYMPTOTIC
NORMALITY OF THE G2 -ESTIMATOR 210 CHAPTER 6. STATISTICAL ESTIMATORS FOR
SOLUTIONS OF SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS 213 1. THE INTEGRAL
REPRESENTATION OF SOLUTIONS OF SLAE 216 2. G-ESTIMATOR FOR THE SOLUTIONS
OF SLAE WHEN OBSERVATIONS OF THE COEFFICIENTS HAVE EQUIVALENT VARIANCES
217 3. CONSISTENT ESTIMATORS FOR THE SOLUTIONS OF SLAE WHEN OBSERVATIONS
OF THE COEFFICIENTS HAVE VARIANCES THAT ARE EQUAL TO THE PRODUCT OF SOME
VALUES 230 4. G8-ESTIMATOR FOR THE SOLUTION OF SLAE WITH A SYMMETRIC
MATRIX OF COEFFICIENTS 232 5. DIFFERENTIAL REPRESENTATION FOR SOLUTIONS
OF SLAE 242 6. REFORM-METHOD. FORMULAE FOR RESOLVENTS 243 7. LIMIT
THEOREMS FOR ENTRIES OF THE RESOLVENT OF RANDOM MATRICES 245 8.
ANALYTICAL CONTINUATION OF ENTRIES OF RESOLVENTS 255 9. BOUNDEDNESS OF
SOLUTIONS OF THE SYSTEM OF G - EQUATIONS 257 10. RANDOM SUBSTITUTION OF
PARAMETERS 258 11. GG-ESTIMATOR FOR THE SOLUTIONS OF SLAE WHEN
OBSERVATIONS OF THE COEFFICIENTS HAVE ARBITRARY VARIANCES 260 12. THE
CONDITIONS FOR CONVERGENCE TO ZERO OF PARAMETERS OF COMPLEX
REGULARIZATION. CONSISTENCY OF THE GG-ESTIMATOR 262 REFERENCES 278 INDEX
283
|
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| author | Girko, Vʼjačeslav Leonidovyč 1946- |
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| dewey-full | 519.5/35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/35 |
| dewey-search | 519.5/35 |
| dewey-sort | 3519.5 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| indexdate | 2024-07-09T17:51:06Z |
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| language | English Russian |
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| spelling | Girko, Vʼjačeslav Leonidovyč 1946- Verfasser (DE-588)1055764976 aut Statistical analysis of observations of increasing dimension by Vyacheslav L. Girko Dordrecht u.a. Kluwer 1995 XXI, 286 S. txt rdacontent n rdamedia nc rdacarrier [Theory and decision library / B] 28 Aus d. Russ. übers. Statistical Analysis of Observations of Increasing Dimension is devoted to the investigation of the limit distribution of the empirical generalized variance, covariance matrices, their eigenvalues and solutions of the system of linear algebraic equations with random coefficients, which are an important function of observations in multidimensional statistical analysis. A general statistical analysis is developed in which observed random vectors may not have density and their components have an arbitrary dependence structure. The methods of this theory have very important advantages in comparison with existing methods of statistical processing. The results have applications in nuclear and statistical physics, multivariate statistical analysis in the theory of the stability of solutions of stochastic differential equations, in control theory of linear stochastic systems, in linear stochastic programming, in the theory of experiment planning. Multivariate analysis Stochastic matrices Stochastische Matrix (DE-588)4057624-3 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 s DE-604 Stochastische Matrix (DE-588)4057624-3 s DE-188 B] [Theory and decision library 28 (DE-604)BV000021513 28 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006895116&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Girko, Vʼjačeslav Leonidovyč 1946- Statistical analysis of observations of increasing dimension Multivariate analysis Stochastic matrices Stochastische Matrix (DE-588)4057624-3 gnd Multivariate Analyse (DE-588)4040708-1 gnd |
| subject_GND | (DE-588)4057624-3 (DE-588)4040708-1 |
| title | Statistical analysis of observations of increasing dimension |
| title_auth | Statistical analysis of observations of increasing dimension |
| title_exact_search | Statistical analysis of observations of increasing dimension |
| title_full | Statistical analysis of observations of increasing dimension by Vyacheslav L. Girko |
| title_fullStr | Statistical analysis of observations of increasing dimension by Vyacheslav L. Girko |
| title_full_unstemmed | Statistical analysis of observations of increasing dimension by Vyacheslav L. Girko |
| title_short | Statistical analysis of observations of increasing dimension |
| title_sort | statistical analysis of observations of increasing dimension |
| topic | Multivariate analysis Stochastic matrices Stochastische Matrix (DE-588)4057624-3 gnd Multivariate Analyse (DE-588)4040708-1 gnd |
| topic_facet | Multivariate analysis Stochastic matrices Stochastische Matrix Multivariate Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006895116&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT girkovʼjaceslavleonidovyc statisticalanalysisofobservationsofincreasingdimension |