Nonparametric analysis of univariate heavy-tailed data: research and practice
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester
Wiley
2007
|
| Series: | Wiley series in probability and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXI, 310 S. graph. Darst. |
| ISBN: | 9780470510872 |
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MARC
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| 245 | 1 | 0 | |a Nonparametric analysis of univariate heavy-tailed data |b research and practice |c Natalia Markovich |
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Record in the Search Index
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| adam_text | NONPARAMETRIC ANALYSIS OF UNIVARIATE HEAVY-TAILED DATA RESEARCH AND
PRACTICE NATALIA MARKOVICH INSTITUTE OF CONTROL SCIENCES, RUSSIAN
ACADEMY OF SCIENCES, MOSCOW, RUSSIA BICKNTIN HL AL BICINTENNIAL JOHN
WILEY &. SONS, LTD CONTENTS PREFACE XI 1 DEFINITIONS AND ROUGH DETECTION
OF TAIL HEAVINESS 1 1.1 DEFINITIONS AND BASIC PROPERTIES OF CLASSES OF
HEAVY-TAILED DISTRIBUTIONS 1 1.2 TAIL INDEX ESTIMATION 6 1.2.1
ESTIMATORS OF A POSITIVE-VALUED TAIL INDEX 6 1.2.2 THE CHOICE OF K IN
HILL S ESTIMATOR 8 1.2.3 ESTIMATORS OF A REAL-VALUED TAIL INDEX 13 1.2.4
ON-LINE ESTIMATION OF THE TAIL INDEX 17 1.3 DETECTION OF TAIL HEAVINESS
AND DEPENDENCE 27 1.3.1 ROUGH TESTS OF TAIL HEAVINESS 27 1.3.2 ANALYSIS
OF WEB TRAFFIC AND TCP FLOW DATA 30 1.3.3 DEPENDENCE DETECTION FROM
UNIVARIATE DATA 42 1.3.4 DEPENDENCE DETECTION FROM BIVARIATE DATA 49
1.3.5 BIVARIATE ANALYSIS OF TCP FLOW DATA 51 1.4 NOTES AND COMMENTS 56
1.5 EXERCISES 57 2 CLASSICAL METHODS OF PROBABILITY DENSITY ESTIMATION
61 2.1 PRINCIPLES OF DENSITY ESTIMATION 61 2.2 METHODS OF DENSITY
ESTIMATION 70 2.2.1 KERNEL ESTIMATORS 70 2.2.2 PROJECTION ESTIMATORS 74
2.2.3 SPLINE ESTIMATORS 76 2.2.4 SMOOTHING METHODS 76 2.2.5 ILLUSTRATIVE
EXAMPLES 83 2.3 KERNEL ESTIMATION FROM DEPENDENT DATA 85 2.3.1 STATEMENT
OF THE PROBLEM 86 2.3.2 NUMERICAL CALCULATION OF THE BANDWIDTH 89 2.3.3
DATA-DRIVEN SELECTION OF THE BANDWIDTH 91 2.4 APPLICATIONS 91 2.4.1
FINANCE: EVALUATION OF MARKET RISK 91 CONTENTS 2.4.2 TELECOMMUNICATIONS
,93 2.4.3 POPULATION ANALYSIS 94 2.5 EXERCISES 95 3 HEAVY-TAILED DENSITY
ESTIMATION 99 3.1 PROBLEMS OF THE ESTIMATION OF HEAVY-TAILED DENSITIES
100 3.2 COMBINED PARAMETRIC-NONPARAMETRIC METHOD 101 3.2.1 NONPARAMETRIC
ESTIMATION OF THE DENSITY BY STRUCTURAL RISK MINIMIZATION 103 3.2.2
ILLUSTRATIVE EXAMPLES 107 3.2.3 WEB DATA ANALYSIS BY A COMBINED
PARAMETRIC-NONPARAMETRIC METHOD 109 3.3 BARRON S ESTIMATOR AND ^ 2
-OPTIMALITY 111 3.4 KERNEL ESTIMATORS WITH VARIABLE BANDWIDTH 113 3.5
RETRANSFORMED NONPARAMETRIC ESTIMATORS 117 3.6 EXERCISES 119 4
TRANSFORMATIONS AND HEAVY-TAILED DENSITY ESTIMATION 123 4.1 PROBLEMS OF
DATA TRANSFORMATIONS 123 4.2 ESTIMATES BASED ON A FIXED TRANSFORMATION
124 4.3 ESTIMATES BASED ON AN ADAPTIVE TRANSFORMATION 128 4.3.1
ESTIMATION ALGORITHM 128 4.3.2 ANALYSIS OF THE ALGORITHM 129 4.3.3
FURTHER REMARKS 133 4.4 ESTIMATING THE ACCURACY OF RETRANSFORMED
ESTIMATES 135 4.5 BOUNDARY KERNEIS 136 4.6 ACCURACY OF A NONVARIABLE
BANDWIDTH KERNEL ESTIMATOR 139 4.7 THE D METHOD FOR A NONVARIABLE
BANDWIDTH KERNEL ESTIMATOR... 141 4.8 THE D METHOD FOR A VARIABLE
BANDWIDTH KERNEL ESTIMATOR 142 4.8.1 METHOD AND RESULTS 142 4.8.2
APPLICATION TO WEB TRAFFIC CHARACTERISTICS 144 4.9 THE O) 2 METHOD FOR
THE PROJECTION ESTIMATOR 147 4.10 EXERCISES 149 5 CLASSIFICATION AND
RETRANSFORMED DENSITY ESTIMATES 151 5.1 CLASSIFICATION AND QUALITY OF
DENSITY ESTIMATION 151 5.2 CONVERGENCE OF THE ESTIMATED PROBABILITY OF
MISCLASSIFICATION.. 154 5.3 SIMULATION STUDY 155 5.4 APPLICATION OF THE
CLASSIFICATION TECHNIQUE TO WEB DATA ANALYSIS 160 5.4.1 INTELLIGENT
BROWSER 160 5.4.2 WEB DATA ANALYSIS BY TRAFFIC CLASSIFICATION 161 5.4.3
WEB PREFETCHING 161 5.5 EXERCISES 161 CONTENTS IX 6 ESTIMATION OF HIGH
QUANTILES 163 6.1 INTRODUCTION 163 6.2 ESTIMATORS OF HIGH QUANTILES 164
6.3 DISTRIBUTION OF HIGH QUANTILE ESTIMATES 167 6.4 SIMULATION STUDY 169
6.4.1 COMPARISON OF HIGH QUANTILE ESTIMATES IN TERMS OF RELATIVE BIAS
AND MEAN SQUARED ERROR 169 6.4.2 COMPARISON OF HIGH QUANTILE ESTIMATES
IN TERMS OF CONFIDENCE INTERVALS 170 6.5 APPLICATION TO WEB TRAFFIC DATA
175 6.6 EXERCISES 176 7 NONPARAMETRIC ESTIMATION OF THE HAZARD RATE
FUNCTION 179 7.1 DEFINITION OF THE HAZARD RATE FUNCTION 180 7.2
STATISTICAL REGULARIZATION METHOD 182 7.3 NUMERICAL SOLUTION OF
ILL-POSED PROBLEMS 185 7.4 ESTIMATION OF THE HAZARD RATE FUNCTION OF
HEAVY-TAILED DISTRIBUTIONS 187 7.5 HAZARD RATE ESTIMATION FOR COMPACTLY
SUPPORTED DISTRIBUTIONS 188 7.5.1 ESTIMATION OF THE HAZARD RATE FROM THE
SIMPLEST EQUATIONS 188 7.5.2 ESTIMATION OF THE HAZARD RATE FROM A
SPECIAL KERNEL EQUATION 193 7.6 ESTIMATION OF THE RATIO OF HAZARD RATES
197 7.6.1 FAILURE TIME DETECTION 199 ~/.6.2 HORMESIS DETECTION 200 7.7
HAZARD RATE ESTIMATION IN TELETRAFFIC THEORY 207 7.7.1 TELETRAFFIC
PROCESSES AT THE PACKET LEVEL 207 7.7.2 ESTIMATION OF THE INTENSITY OF A
NONHOMOGENEOUS POISSON PROCESS 208 7.8 SEMI-MARKOV MODELING IN
TELETRAFFIC ENGINEERING 210 7.8.1 THE GILBERT-ELLIOTT MODEL 210 7.8.2
ESTIMATION OF A RETRIAL PROCESS 212 7.9 EXERCISES 217 8 NONPARAMETRIC
ESTIMATION OF THE RENEWAL FUNCTION 219 8.1 TRAFFIC MODELING BY RECURRENT
MARKED POINT PROCESSES 220 8.2 INTRODUCTION TO RENEWAL FUNCTION
ESTIMATION 221 8.3 HISTOGRAM-TYPE ESTIMATOR OF THE RENEWAL FUNCTION 224
8.4 CONVERGENCE OF THE HISTOGRAM-TYPE ESTIMATOR 225 8.5 SELECTION OF K
BY A BOOTSTRAP METHOD 228 8.6 SELECTION OF K BY A PLOT 232 8.7
SIMULATION STUDY 234 8.8 APPLICATION TO THE INTER-ARRIVAL TIMES OF TCP
CONNECTIONS 245 X CONTENTS 8.9 CONCLUSIONS AND DISCUSSION 247 8.10
EXERCISES 248 APPENDICES A PROOFS OF CHAPTER 2 251 B PROOFS OF CHAPTER 4
253 C PROOFS OF CHAPTER 5 267 D PROOFS OF CHAPTER 6 271 E PROOFS OF
CHAPTER 7 275 F PROOFS OF CHAPTER 8 285 LIST OF MAIN SYMBOLS AND
ABBREVIATIONS 291 REFERENCES 295 INDEX 307
|
| adam_txt |
NONPARAMETRIC ANALYSIS OF UNIVARIATE HEAVY-TAILED DATA RESEARCH AND
PRACTICE NATALIA MARKOVICH INSTITUTE OF CONTROL SCIENCES, RUSSIAN
ACADEMY OF SCIENCES, MOSCOW, RUSSIA BICKNTIN HL AL BICINTENNIAL JOHN
WILEY &. SONS, LTD CONTENTS PREFACE XI 1 DEFINITIONS AND ROUGH DETECTION
OF TAIL HEAVINESS 1 1.1 DEFINITIONS AND BASIC PROPERTIES OF CLASSES OF
HEAVY-TAILED DISTRIBUTIONS 1 1.2 TAIL INDEX ESTIMATION 6 1.2.1
ESTIMATORS OF A POSITIVE-VALUED TAIL INDEX 6 1.2.2 THE CHOICE OF K IN
HILL'S ESTIMATOR 8 1.2.3 ESTIMATORS OF A REAL-VALUED TAIL INDEX 13 1.2.4
ON-LINE ESTIMATION OF THE TAIL INDEX 17 1.3 DETECTION OF TAIL HEAVINESS
AND DEPENDENCE 27 1.3.1 ROUGH TESTS OF TAIL HEAVINESS 27 1.3.2 ANALYSIS
OF WEB TRAFFIC AND TCP FLOW DATA 30 1.3.3 DEPENDENCE DETECTION FROM
UNIVARIATE DATA 42 1.3.4 DEPENDENCE DETECTION FROM BIVARIATE DATA 49
1.3.5 BIVARIATE ANALYSIS OF TCP FLOW DATA 51 1.4 NOTES AND COMMENTS 56
1.5 EXERCISES 57 2 CLASSICAL METHODS OF PROBABILITY DENSITY ESTIMATION
61 2.1 PRINCIPLES OF DENSITY ESTIMATION 61 2.2 METHODS OF DENSITY
ESTIMATION 70 2.2.1 KERNEL ESTIMATORS 70 2.2.2 PROJECTION ESTIMATORS 74
2.2.3 SPLINE ESTIMATORS 76 2.2.4 SMOOTHING METHODS 76 2.2.5 ILLUSTRATIVE
EXAMPLES 83 2.3 KERNEL ESTIMATION FROM DEPENDENT DATA 85 2.3.1 STATEMENT
OF THE PROBLEM 86 2.3.2 NUMERICAL CALCULATION OF THE BANDWIDTH 89 2.3.3
DATA-DRIVEN SELECTION OF THE BANDWIDTH 91 2.4 APPLICATIONS 91 2.4.1
FINANCE: EVALUATION OF MARKET RISK 91 CONTENTS 2.4.2 TELECOMMUNICATIONS
,93 2.4.3 POPULATION ANALYSIS 94 2.5 EXERCISES 95 3 HEAVY-TAILED DENSITY
ESTIMATION 99 3.1 PROBLEMS OF THE ESTIMATION OF HEAVY-TAILED DENSITIES
100 3.2 COMBINED PARAMETRIC-NONPARAMETRIC METHOD 101 3.2.1 NONPARAMETRIC
ESTIMATION OF THE DENSITY BY STRUCTURAL RISK MINIMIZATION 103 3.2.2
ILLUSTRATIVE EXAMPLES 107 3.2.3 WEB DATA ANALYSIS BY A COMBINED
PARAMETRIC-NONPARAMETRIC METHOD 109 3.3 BARRON'S ESTIMATOR AND ^ 2
-OPTIMALITY 111 3.4 KERNEL ESTIMATORS WITH VARIABLE BANDWIDTH 113 3.5
RETRANSFORMED NONPARAMETRIC ESTIMATORS 117 3.6 EXERCISES 119 4
TRANSFORMATIONS AND HEAVY-TAILED DENSITY ESTIMATION 123 4.1 PROBLEMS OF
DATA TRANSFORMATIONS 123 4.2 ESTIMATES BASED ON A FIXED TRANSFORMATION
124 4.3 ESTIMATES BASED ON AN ADAPTIVE TRANSFORMATION 128 4.3.1
ESTIMATION ALGORITHM 128 4.3.2 ANALYSIS OF THE ALGORITHM 129 4.3.3
FURTHER REMARKS 133 4.4 ESTIMATING THE ACCURACY OF RETRANSFORMED
ESTIMATES 135 4.5 BOUNDARY KERNEIS 136 4.6 ACCURACY OF A NONVARIABLE
BANDWIDTH KERNEL ESTIMATOR 139 4.7 THE D METHOD FOR A NONVARIABLE
BANDWIDTH KERNEL ESTIMATOR. 141 4.8 THE D METHOD FOR A VARIABLE
BANDWIDTH KERNEL ESTIMATOR 142 4.8.1 METHOD AND RESULTS 142 4.8.2
APPLICATION TO WEB TRAFFIC CHARACTERISTICS 144 4.9 THE O) 2 METHOD FOR
THE PROJECTION ESTIMATOR 147 4.10 EXERCISES 149 5 CLASSIFICATION AND
RETRANSFORMED DENSITY ESTIMATES 151 5.1 CLASSIFICATION AND QUALITY OF
DENSITY ESTIMATION 151 5.2 CONVERGENCE OF THE ESTIMATED PROBABILITY OF
MISCLASSIFICATION. 154 5.3 SIMULATION STUDY 155 5.4 APPLICATION OF THE
CLASSIFICATION TECHNIQUE TO WEB DATA ANALYSIS 160 5.4.1 INTELLIGENT
BROWSER 160 5.4.2 WEB DATA ANALYSIS BY TRAFFIC CLASSIFICATION 161 5.4.3
WEB PREFETCHING 161 5.5 EXERCISES 161 CONTENTS IX 6 ESTIMATION OF HIGH
QUANTILES 163 6.1 INTRODUCTION 163 6.2 ESTIMATORS OF HIGH QUANTILES 164
6.3 DISTRIBUTION OF HIGH QUANTILE ESTIMATES 167 6.4 SIMULATION STUDY 169
6.4.1 COMPARISON OF HIGH QUANTILE ESTIMATES IN TERMS OF RELATIVE BIAS
AND MEAN SQUARED ERROR 169 6.4.2 COMPARISON OF HIGH QUANTILE ESTIMATES
IN TERMS OF CONFIDENCE INTERVALS 170 6.5 APPLICATION TO WEB TRAFFIC DATA
175 6.6 EXERCISES 176 7 NONPARAMETRIC ESTIMATION OF THE HAZARD RATE
FUNCTION 179 7.1 DEFINITION OF THE HAZARD RATE FUNCTION 180 7.2
STATISTICAL REGULARIZATION METHOD 182 7.3 NUMERICAL SOLUTION OF
ILL-POSED PROBLEMS 185 7.4 ESTIMATION OF THE HAZARD RATE FUNCTION OF
HEAVY-TAILED DISTRIBUTIONS 187 7.5 HAZARD RATE ESTIMATION FOR COMPACTLY
SUPPORTED DISTRIBUTIONS 188 7.5.1 ESTIMATION OF THE HAZARD RATE FROM THE
SIMPLEST EQUATIONS 188 7.5.2 ESTIMATION OF THE HAZARD RATE FROM A
SPECIAL KERNEL EQUATION 193 7.6 ESTIMATION OF THE RATIO OF HAZARD RATES
197 7.6.1 FAILURE TIME DETECTION 199 ~/.6.2 HORMESIS DETECTION 200 7.7
HAZARD RATE ESTIMATION IN TELETRAFFIC THEORY 207 7.7.1 TELETRAFFIC
PROCESSES AT THE PACKET LEVEL 207 7.7.2 ESTIMATION OF THE INTENSITY OF A
NONHOMOGENEOUS POISSON PROCESS 208 7.8 SEMI-MARKOV MODELING IN
TELETRAFFIC ENGINEERING 210 7.8.1 THE GILBERT-ELLIOTT MODEL 210 7.8.2
ESTIMATION OF A RETRIAL PROCESS 212 7.9 EXERCISES 217 8 NONPARAMETRIC
ESTIMATION OF THE RENEWAL FUNCTION 219 8.1 TRAFFIC MODELING BY RECURRENT
MARKED POINT PROCESSES 220 8.2 INTRODUCTION TO RENEWAL FUNCTION
ESTIMATION 221 8.3 HISTOGRAM-TYPE ESTIMATOR OF THE RENEWAL FUNCTION 224
8.4 CONVERGENCE OF THE HISTOGRAM-TYPE ESTIMATOR 225 8.5 SELECTION OF K
BY A BOOTSTRAP METHOD 228 8.6 SELECTION OF K BY A PLOT 232 8.7
SIMULATION STUDY 234 8.8 APPLICATION TO THE INTER-ARRIVAL TIMES OF TCP
CONNECTIONS 245 X CONTENTS 8.9 CONCLUSIONS AND DISCUSSION 247 8.10
EXERCISES 248 APPENDICES A PROOFS OF CHAPTER 2 251 B PROOFS OF CHAPTER 4
253 C PROOFS OF CHAPTER 5 267 D PROOFS OF CHAPTER 6 271 E PROOFS OF
CHAPTER 7 275 F PROOFS OF CHAPTER 8 285 LIST OF MAIN SYMBOLS AND
ABBREVIATIONS 291 REFERENCES 295 INDEX 307 |
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| spelling | Markovič, Natal'ja M. Verfasser aut Nonparametric analysis of univariate heavy-tailed data research and practice Natalia Markovich Chichester Wiley 2007 XXI, 310 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Nonparametric statistics Research Nichtparametrische Statistik (DE-588)4226777-8 gnd rswk-swf Nichtparametrische Statistik (DE-588)4226777-8 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016171842&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Markovič, Natal'ja M. Nonparametric analysis of univariate heavy-tailed data research and practice Nonparametric statistics Research Nichtparametrische Statistik (DE-588)4226777-8 gnd |
| subject_GND | (DE-588)4226777-8 |
| title | Nonparametric analysis of univariate heavy-tailed data research and practice |
| title_auth | Nonparametric analysis of univariate heavy-tailed data research and practice |
| title_exact_search | Nonparametric analysis of univariate heavy-tailed data research and practice |
| title_exact_search_txtP | Nonparametric analysis of univariate heavy-tailed data research and practice |
| title_full | Nonparametric analysis of univariate heavy-tailed data research and practice Natalia Markovich |
| title_fullStr | Nonparametric analysis of univariate heavy-tailed data research and practice Natalia Markovich |
| title_full_unstemmed | Nonparametric analysis of univariate heavy-tailed data research and practice Natalia Markovich |
| title_short | Nonparametric analysis of univariate heavy-tailed data |
| title_sort | nonparametric analysis of univariate heavy tailed data research and practice |
| title_sub | research and practice |
| topic | Nonparametric statistics Research Nichtparametrische Statistik (DE-588)4226777-8 gnd |
| topic_facet | Nonparametric statistics Research Nichtparametrische Statistik |
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