Non-parametric statistical diagnosis: problems and methods
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
2000
|
| Series: | Mathematics and its applications
509 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 452 S. graph. Darst. |
| ISBN: | 0792363280 |
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Record in the Search Index
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| adam_text | NON-PARAMETRIC STATISTICAL DIAGNOSIS PROBLEMS AND METHODS BY B.E.
BRODSKY STATE UNIVERSITY, HIGHER SCHOOL OF ECONOMICS, MOSCOW, RUSSIA AND
B.S. DARKHOVSKY^ INSTITUTE FOR SYSTEMS ANALYSIS, RUSSIAN ACADEMY OF
SCIENCES, MOSCOW, RUSSIA KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON /
LONDON TABLE OF CONTENTS PREFACE IX PART 1. THEORY 1 CHAPTERJ 1
PRELIMINARY CONSIDERATIONS 3 1.1 NECESSARY RESULTS FROM THE THEORY OF
RANDOM PROCESSES 3 1.1.1 MIXING CONDITIONS 3 1.1.2 SOME INEQUALITIES.
CONVERGENCE OF RANDOM VARIABLES 8 1.1.3 ERGODICITY OF RANDOM SEQUENCES
11 1.1.4 THE WIENER PROCESS AND SOME FUNCTIONALS RELATED TO IT 12 1.1.5
WEAK CONVERGENCE 16 1.1.6 PROBABILISTIC INEQUALITIES FOR MAXIMUM OF SUMS
OF RANDOM VARIABLES 29 1.1.7 MARTINGALES. MARKOV S MOMENTS. WALD S
IDENTITY 35 1.2 NECESSARY RESULTS FROM THE THEORY OF RANDOM FIELDS 37
1.3 NECESSARY RESULTS FROM OPTIMIZATION THEORY 49 1.3.1 OPTIMALITY
CONDITIONS FOR SMOOTH FINITE-DIMENSIONAL PROBLEMS OF MATHEMATICAL
PROGRAMMING 49 1.3.2 SOME PROPERTIES OF FUNCTIONALS OF THE MAXIMUM TYPE
53 1.4 MAIN IDEAS OF THE NONPARAMETRIC APPROACH TO THE PROBLEMS OF
STATISTICAL DIAGNOSIS 57 1.4.1 RANDOM PROCESSES 58 1.4.2 RANDOM FIELDS
63 1.5 MAIN ASSUMPTIONS 66 1.5.1 RANDOM PROCESSES 67 1.5.2 RANDOM FIELDS
77 VI CONTENTS CHAPTER 2 STATE OF THE ART REVIEW 83 2.1 INTRODUCTION 83
2.2 RETROSPECTIVE METHODS OF STATISTICAL DIAGNOSIS 85 2.2.1 CHANGE-POINT
PROBLEMS 85 2.2.2 CONTAMINATION PROBLEMS 107 2.3 SEQUENTIAL METHODS OF
STATISTICAL DIAGNOSIS 109 2.4 PROBLEMS OF STATISTICAL DIAGNOSIS FOR
RANDOM FIELDS 122 CHAPTER 3 RETROSPECTIVE METHODS OF STATISTICAL
DIAGNOSIS FOR RANDOM SEQUENCES: CHANGE-POINT PROBLEMS 127 3.1 STATEMENT
OF THE GENERAL RETROSPECTIVE CHANGE-POINT PROBLEM FOR A RANDOM SEQUENCE.
VARIANTS OF PROBLEMS UNDER CONSIDERATION .... 127 3.2 A SINGLE ABRUPT
CHANGE-POINT 130 3.2.1 AN ABRUPT CHANGE OF THE FUNCTION IP 130 3.2.2 AN
ABRUPT CHANGE OF COEFFICIENTS OF THE LINEAR FUNCTIONAL REGRESSION 134
3.2.3 AN ABRUPT CHANGE OF (K + L)-TH DERIVATIVE OF THE FUNCTION IP / 145
3.3 MULTIPLE ABRUPT CHANGE-POINTS 146 3.3.1 ABRUPT CHANGES OF THE
FUNCTION IP 146 3.3.2 ABRUPT CHANGES OF COEFFICIENTS OF THE LINEAR
FUNCTIONAL REGRESSION 151 3.4 GRADUAL CHANGE-POINT PROBLEMS 155 3.4.1 A
SINGLE GRADUAL CHANGE OF THE FUNCTION 155 3.5 ASYMPTOTIC ANALYSIS OF
CHANGE-POINT ESTIMATES 169 3.6 A PRIORI LOW BOUNDS IN RETROSPECTIVE
CHANGE-POINT PROBLEMS 182 3.6.1 THE RAO-CRAMER TYPE INEQUALITY 182 3.6.2
ASYMPTOTIC LOW BOUND IN THE SINGLE CHANGE-POINT PROBLEM 186 3.6.3
ASYMPTOTIC LOW BOUND IN THE MULTIPLE CHANGE-POINT PROBLEM ... 191 3.6.4
ASYMPTOTIC LOW BOUND IN THE SINGLE CHANGE-POINT PROBLEM FOR REGRESSION
RELATIONSHIPS 195 3.7 CONCLUSION 197 BIBLIOGRAPHICAL COMMENTS 200
CHAPTER 4 RETROSPECTIVE METHODS OF STATISTICAL DIAGNOSIS FOR RANDOM
PROCESSES: CONTAMINATION PROBLEMS 201 4.1 INTRODUCTION 201 4.2 PROBLEM
OF MEAN VALUE CONTAMINATION 203 4.3 GENERALISATIONS 209 4.3.1 GENERAL
REMARKS 209 4.3.2 CONTAMINATION PROBLEMS FOR REGRESSION MODEIS 212
CONTENTS VII 4.4 A PRIORI ESTIMATES IN CONTAMINATION PROBLEMS 213 4.5
MONTE CARLO EXPERIMENTS 216 4.6 CONCLUSION 218 CHAPTER 5 SEQUENTIAL
METHODS OF STATISTICAL DIAGNOSIS ... .219 5.1 INTRODUCTION 219 5.2
CHANGE-POINT PROBLEM 223 5.2.1 QUALITY CHARACTERISTICS OF SEQUENTIAL
METHODS 224 5.2.2 A PRIORI ESTIMATES OF QUALITY OF SEQUENTIAL
CHANGE-POINT DETECTION METHODS 247 5.2.3 ASYMPTOTIC COMPARATIVE ANALYSIS
OF SEQUENTIAL CHANGE-POINT DETECTION METHODS 253 5.3 PROBLEM OF EARLY
DETECTION 281 5.3.1 FORMULATION OF THE PROBLEM 281 5.3.2
CHARACTERISTICS OF METHODS IN THE PROBLEM OF EARLY DETECTION 283 5.3.3
A PRIORI ESTIMATES OF QUALITY FOR EARLY DETECTION METHODS 285 5.3.4
ANALYSIS OF ASYMPTOTIC OPTIMALITY OF EARLY DETECTION METHODS 290 5.3.5
ROBUSTNESS OF SEQUENTIAL METHODS 292 5.4 CONCLUSION 297 CHAPTER 6
STATISTICAL DIAGNOSIS PROBLEMS FOR RANDOM FIELDS 299 6.1 RETROSPECTIVE
DIAGNOSIS PROBLEMS FOR RANDOM FIELDS 300 6.1.1 PROBLEM A 303 6.1.2
PROBLEM B 309 6.1.3 A PRIORI ESTIMATES OF QUALITY IN RETROSPECTIVE
DIAGNOSIS PROBLEMS FOR RANDOM FIELDS 317 6.2 SEQUENTIAL DIAGNOSIS
PROBLEMS FOR RANDOM FIELDS 322 6.3 CONTAMINATION PROBLEMS FOR RANDOM
FIELDS 324 6.4 CONCLUSION 328 PART 2. APPLICATIONS 331 CHAPTER 7
APPLICATION OF THE CHANGE-POINT ANALYSIS TO INVESTIGATION OF THE BRAIN
ELECTRICAL ACTIVITY 333 7.1 INTRODUCTION 333 7.2 GENERAL DESCRIPTION OF
APPROACHES TO QUANTITATIVE FEATURE EXTRACTION FROM THE EEG SIGNAL 336
7.3 NONSTATIONARITIES IN EEGS. METHODS OF SEGMENTATION OF THE EEG SIGNAL
337 VIII CONTENTS 7.3.1 SEGMENTATION OF THE EEG USING FIXED INTERVALS
338 7.3.2 PARAMETRIC SEGMENTATION OF THE EEG 339 7.3.3 NONPARAMETRIC
APPROACHES TO THE DESCRIPTION OF PIECEWISE STATIONARY STRUCTURE OF EEG
342 7.4 EXPERIMENTAL RESULTS 346 7.4.1 CHANGE-POINT DETECTION ALGORITHM
PERFORMANCE WITH REAL EEG DATA 349 7.4.2 CHANGE-POINTS IN EEG COMPONENTS
WITH DIFFERENT PATTERN 350 7.4.3 DETECTION OF CHANGE-POINTS AT DIFFERENT
LEVELS OF THE HIERARCHY OF EEG SEGMENTAL DESCRIPTIONS 352 7.4.4
CHANGE-POINTS IN MULTI-CHANNEL EEG 357 7.4.5 THE APPROACH TO THE
ANALYSIS OF CHANGE-POINT SYNCHRONIZATION IN MULTI-CHANNEL EEG 362 7.4.6
CHANGE-POINT SYNCHRONIZATION IN PAIRS OF EEG CHANNELS 365 7.4.7
MULTICHANNEL ANALYSIS OF SPATIAL SYNCHRONIZATION OF THE CHANGE-POINTS
372 7.5 SOME GENERAL THEORETICAL CONSIDERATIONS 378 7.5.1 UNSOLVED
PROBLEMS AND NEW PROSPECTS 378 7.5.2 CHANGE-POINT BASED ANALYSIS OF THE
SYNCHRONIZATION BETWEEN SIGNALS OR SIGNAL COMPONENTS 380 7.6 OTHER
PROSPECTS OF THE CHANGE-POINT BASED ANALYSIS 384 7.7 CONCLUSION 386
CHAPTER 8 METHODS OF STATISTICAL DIAGNOSIS IN ECONOMIC AND FINANCIAL
SYSTEMS 389 8.1 INTRODUCTION 389 8.2. ECONOMETRIC MODEIS WITH STRUCTURAL
BREAKS 390 8.3 ECONOMETRIC MODEIS WITH CONTAMINATION EFFECTS 397 8.4
EARLY DETECTION OF CRISES IN ECONOMIC AND FINANCIAL SYSTEMS 399 8.5
CONCLUSION 405 APPENDIX. ALGORITHMS OF STATISTICAL DIAGNOSIS 407
BIBLIOGRAPHY 417 AUTHOR INDEX 445 SUBJECT INDEX 447 MAIN NOTATIONS AND
ABBREVIATIONS 451
|
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| author_facet | Brodskij, Boris E. Darchovskij, Boris S. |
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.54 |
| dewey-search | 519.54 |
| dewey-sort | 3519.54 |
| dewey-tens | 510 - Mathematics |
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| physical | XV, 452 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
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| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Brodskij, Boris E. Verfasser aut Non-parametric statistical diagnosis problems and methods by B. E. Brodsky and B. S. Darkhovsky Dordrecht [u.a.] Kluwer 2000 XV, 452 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 509 Nichtparametrische Statistik (DE-588)4226777-8 gnd rswk-swf Nichtparametrischer Test (DE-588)4075372-4 gnd rswk-swf Change-point-Problem (DE-588)4598971-0 gnd rswk-swf Nichtparametrischer Test (DE-588)4075372-4 s Change-point-Problem (DE-588)4598971-0 s Nichtparametrische Statistik (DE-588)4226777-8 s DE-604 Darchovskij, Boris S. Verfasser aut Mathematics and its applications 509 (DE-604)BV008163334 509 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019944127&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brodskij, Boris E. Darchovskij, Boris S. Non-parametric statistical diagnosis problems and methods Mathematics and its applications Nichtparametrische Statistik (DE-588)4226777-8 gnd Nichtparametrischer Test (DE-588)4075372-4 gnd Change-point-Problem (DE-588)4598971-0 gnd |
| subject_GND | (DE-588)4226777-8 (DE-588)4075372-4 (DE-588)4598971-0 |
| title | Non-parametric statistical diagnosis problems and methods |
| title_auth | Non-parametric statistical diagnosis problems and methods |
| title_exact_search | Non-parametric statistical diagnosis problems and methods |
| title_full | Non-parametric statistical diagnosis problems and methods by B. E. Brodsky and B. S. Darkhovsky |
| title_fullStr | Non-parametric statistical diagnosis problems and methods by B. E. Brodsky and B. S. Darkhovsky |
| title_full_unstemmed | Non-parametric statistical diagnosis problems and methods by B. E. Brodsky and B. S. Darkhovsky |
| title_short | Non-parametric statistical diagnosis |
| title_sort | non parametric statistical diagnosis problems and methods |
| title_sub | problems and methods |
| topic | Nichtparametrische Statistik (DE-588)4226777-8 gnd Nichtparametrischer Test (DE-588)4075372-4 gnd Change-point-Problem (DE-588)4598971-0 gnd |
| topic_facet | Nichtparametrische Statistik Nichtparametrischer Test Change-point-Problem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019944127&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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