Dependence modeling with copulas:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
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Boca Raton, Fla. [u.a.]
CRC Press
2015
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| Series: | Monographs on statistics and applied probability
134 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Item Description: | "A CRC title.". - Includes bibliographical references and index |
| Physical Description: | XVIII, 462 S. graph. Darst., Kt. |
| ISBN: | 9781466583221 |
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| adam_text | DEPENDENCE MODELLING WITH COPULAS
/ JOE, HARRY.
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
A CHAPTER 1. INTRODUCTION
CHAPTER 2. BASICS: DEPENDENCE, TAIL BEHAVIOR AND ASYMMETRIES
CHAPTER 3. COPULA CONSTRUCTION METHODS
CHAPTER 4. PARAMETRIC COPULA FAMILIES AND PROPERTIES
CHAPTER 5. INFERENCE, DIAGNOSTICS AND MODEL SELECTION
CHAPTER 6. COMPUTING AND ALGORITHMS
CHAPTER 7. APPLICATIONS AND DATA EXAMPLES
CHAPTER 8. THEOREMS FOR PROPERTIES OF COPULAS
APPENDIX A. LAPLACE TRANSFORMS AND ARCHIMEDEAN GENERATORS
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
Contents
Preface xiii
Notation xv
1 Introduction 1
1.1 Dependence modeling 1
1.2 Early research for multivariate non-Gaussian 2
1.3 Copula representation for a multivariate distribution 7
1.4 Data examples: scatterplots and semi-correlations 9
1.5 Likelihood analysis and model comparisons 15
1.5.1 A brief summary of maximum likelihood 16
1.5.2 Two-stage estimation for copula models 16
1.5.3 Likelihood analysis for continuous data: insurance loss 17
1.5.4 Likelihood analysis for discrete data: ordinal response 19
1.6 Copula models versus alternative multivariate models 23
1.7 Terminology for multivariate distributions with U(0?1) margins 23
1.8 Copula constructions and properties 24
2 Basics: dependence, tail behavior and asymmetries 25
2.1 Multivariate cdfs and their conditional distributions 26
2.1.1 Conditions for multivariate cdfs 26
2.1.2 Absolutely continuous and singular components 28
2.1.3 Conditional cdfs 29
2.1.4 Mixture models and conditional independence models 31
2.1.5 Power of a cdf or survival function 32
2.2 Laplace transforms 33
2.3 Extreme value theory 34
2.4 Tail heaviness 36
2.5 Probability integral transform 38
2.6 Multivariate Gaussian/normal 38
2.7 Elliptical and multivariate t distributions 41
2.8 Multivariate dependence concepts 45
2.8.1 Positive quadrant and orthant dependence 45
2.8.2 Stochastically increasing positive dependence 46
2.8.3 Right-tail increasing and left-tail decreasing 46
2.8.4 Associated random variables 46
2.8.5 Total positivity of order 2 47
2.9 Frechet classes and Frechet bounds, given univariate margins 47
2.10 Frechet classes given higher order margins 50
2.11 Concordance and other dependence orderings 51
2.12 Measures of bivariate monotone association 53
2.12.1 KendalPs tau 55
CONTENTS
viii
2.12.2 Spearman’s rank correlation 56
2.12.3 Blomqvist’s beta 57
2.12.4 Correlation of normal scores 58
2.12.5 Auxiliary results for dependence measures 58
2.12.6 Magnitude of asymptotic variance of measures of associations 59
2.12.7 Measures of association for discrete/ordinal variables 60
2.13 Tail dependence 62
2.14 Tail asymmetry 64
2.15 Measures of bivariate asymmetry 65
2.16 Tail order 67
2.16.1 Tail order function and copula density 68
2.17 Semi-correlations of normal scores for a bivariate copula 70
2.18 Tail dependence functions 73
2.19 Strength of dependence in tails and boundary conditional cdfs 80
2.20 Conditional tail expectation for bivariate distributions 80
2.21 Tail comonotonicity 84
2.22 Summary for analysis of properties of copulas 84
3 Copula construction methods 85
3.1 Overview of dependence structures and desirable properties 86
3.2 Archimedean copulas based on frailty/resilience 89
3.3 Archimedean copulas based on Williamson transform 93
3.4 Hierarchical Archimedean and dependence 95
3.5 Mixtures of max-id 98
3.6 Another limit for max-id distributions 102
3.7 Frechet class given bivariate margins 106
3.8 Mixtures of conditional distributions 106
3.9 Vine copulas or pair-copula constructions 107
3.9.1 Vine sequence of conditional distributions 108
3.9.2 Vines as graphical models 110
3.9.3 Vine distribution: conditional distributions and joint density 112
3.9.4 Vine array 114
3.9.5 Vines with some or all discrete marginal distributions 115
3.9.6 Truncated vines 117
3.9.7 Multivariate distributions for which the simplifying assumption holds 118
3.9.8 Vine equivalence classes 126
3.9.9 Historical background of vines 127
3.10 Factor copula models 128
3.10.1 Continuous response 128
3.10.2 Discrete ordinal response 132
3.10.3 Mixed continuous and ordinal response 135
3.10.4 t-Copula with factor correlation matrix structure 135
3.11 Combining models for different groups of variables 136
3.11.1 Bi-factor copula model 137
3.11.2 Nested dependent latent variables 137
3.11.3 Dependent clusters with conditional independence 138
3.12 Nonlinear structural equation models 140
3.13 Truncated vines, factor models and graphical models 143
3.14 Copulas for stationary time series models 144
3.15 Multivariate extreme value distributions 148
3.16 Multivariate extreme value distributions with factor structure 150
3.17 Other multivariate models 151
CONTENTS ix
3.17.1 Analogy of Archimedean and elliptical 152
3.17.2 Other constructions 153
3.18 Operations to get additional copulas 155
3.19 Summary for construction methods 158
4 Parametric copula families and properties 159
4.1 Summary of parametric copula families 160
4.2 Properties of classes of bivariate copulas 162
4.3 Gaussian 163
4.3.1 Bivariate Gaussian copula 163
4.3.2 Multivariate Gaussian copula 164
4.4 Plackett 164
4.5 Copulas based on the logarithmic series LT 165
4.5.1 Bivariate Frank 165
4.5.2 Multivariate Frank extensions 166
4.6 Copulas based on the gamma LT 168
4.6.1 Bivariate Mardia-Takahasi-Clayton-Cook-Johnson 168
4.6.2 Multivariate MTCJ extensions 168
4.7 Copulas based on the Sibuya LT 170
4.7.1 Bivariate Joe/B5 170
4.7.2 Multivariate extensions with Sibuya LT 171
4.8 Copulas based on the positive stable LT 171
4.8.1 Bivariate Gumbel 171
4.8.2 Multivariate Gumbel extensions 172
4.9 Galambos extreme value 174
4.9.1 Bivariate Galambos copula 174
4.9.2 Multivariate Galambos extensions 175
4.10 Hiisler-Reiss extreme value 175
4.10.1 Bivariate Hiisler-Reiss 176
4.10.2 Multivariate Hiisler-Reiss 176
4.11 Archimedean with LT that is integral of positive stable 177
4.11.1 Bivariate copula in Joe and Ma, 2000 177
4.11.2 Multivariate extension 180
4.12 Archimedean based on LT of inverse gamma 180
4.13 Multivariate t*, 181
4.14 Marshall-Olkin multivariate exponential 182
4.14.1 Bivariate Marshall-Olkin 182
4.14.2 Multivariate Marshall-Olkin exponential and extensions 184
4.15 Asymmetric Gumbel/Galambos copulas 185
4.15.1 Asymmetric Gumbel with Marshall-Olkin at boundary 185
4.15.2 Asymmetric Gumbel based on deHaan representation 186
4.16 Extreme value limit of multivariate tu 189
4.16.1 Bivariate t-EV 189
4.17 Copulas based on the gamma stopped positive stable LT 190
4.17.1 Bivariate BB1: Joe and Hu, 1996 190
4.17.2 BB1: range of pairs of dependence measures 192
4.17.3 Multivariate extensions of BB1 193
4.18 Copulas based on the gamma stopped gamma LT 193
4.18.1 Bivariate BB2: Joe and Hu, 1996 193
4.19 Copulas based on the positive stable stopped gamma LT 195
4.19.1 Bivariate BB3: Joe and Hu, 1996 195
4.20 Gamma power mixture of Galambos 196
X
CONTENTS
4.20.1 Bivariate BB4: Joe and Hu, 1996 197
4.20.2 Multivariate extensions of BB4 198
4.21 Positive stable power mixture of Galambos 199
4.21.1 Bivariate BB5: Joe and Hu, 1996 199
4.22 Copulas based on the Sibuya stopped positive stable LT 200
4.22.1 Bivariate BB6: Joe and Hu, 1996 200
4.23 Copulas based on the Sibuya stopped gamma LT 201
4.23.1 Bivariate BB7: Joe and Hu, 1996 202
4.24 Copulas based on the generalized Sibuya LT 203
4.24.1 Bivariate BB8; Joe 1993 204
4.25 Copulas based on the tilted positive stable LT 205
4.25.1 Bivariate BB9 or Crowder 205
4.26 Copulas based on the shifted negative binomial LT 206
4.26.1 Bivariate BB10 206
4.27 Multivariate GB2 distribution and copula 208
4.28 Factor models based on convolution-closed families 210
4.29 Morgenstern or FGM 212
4.29.1 Bivariate FGM 213
4.29.2 Multivariate extensions of FGM 213
4.30 Frechet’s convex combination 214
4.31 Additional parametric copula families 214
4.31.1 Archimedean copula: LT is integral of Mittag-Lefiler LT 215
4.31.2 Archimedean copula based on positive stable stopped Sibuya LT 216
4.31.3 Archimedean copula based on gamma stopped Sibuya LT 216
4.31.4 3-parameter families with a power parameter 217
4.32 Dependence comparisons 220
4.33 Summary for parametric copula families 222
5 Inference, diagnostics and model selection 223
5.1 Parametric inference for copulas 223
5.2 Likelihood inference 225
5.3 Log-likelihood for copula models 226
5.4 Maximum likelihood: asymptotic theory 227
5.5 Inference functions and estimating equations 228
5.5.1 Resampling methods for interval estimates 231
5.6 Composite likelihood 232
5.7 Kullback-Leibler divergence 234
5.7.1 Sample size to distinguish two densities 235
5.7.2 Jeffreys’ divergence and KL sample size 236
5.7.3 Kullback-Leibler divergence and maximum likelihood 240
5.7.4 Discretized multivariate Gaussian 242
5.8 Initial data analysis for copula models 243
5.8.1 Univariate models 244
5.8.2 Dependence structure 245
5.8.3 Joint tails 246
5.9 Copula pseudo likelihood, sensitivity analysis 246
5.10 Non-parametric inference 247
5.10.1 Empirical copula 247
5.10.2 Estimation of functionals of a copula 248
5.10.3 Non-parametric estimation of low-dimensional copula 250
5.11 Diagnostics for conditional dependence 251
5.12 Diagnostics for adequacy of fit 254
CONTENTS xi
5.12.1 Continuous variables 255
5.12.2 Multivariate discrete and ordinal categorical 256
5.13 Vuong’s procedure for parametric model comparisons 257
5.14 Summary for inference 258
6 Computing and algorithms 259
6.1 Roots of nonlinear equations 260
6.2 Numerical optimization and maximum likelihood 261
6.3 Numerical integration and quadrature 262
6.4 Interpolation 264
6.5 Numerical methods involving matrices 265
6.6 Graphs and spanning trees 266
6.7 Computation of r, ps and pN for copulas 267
6.8 Computation of empirical Kendall’s r 269
6.9 Simulation from multivariate distributions and copulas 270
6.9.1 Conditional method or Rosenblatt transform 270
6.9.2 Simulation with reflected uniform random variables 271
6.9.3 Simulation from product of cdfs 272
6.9.4 Simulation from Archimedean copulas 272
6.9.5 Simulation from mixture of max-id 273
6.9.6 Simulation from multivariate extreme value copulas 274
6.10 Likelihood for vine copula 274
6.11 Likelihood for factor copula 279
6.12 Copula derivatives for factor and vine copulas 281
6.13 Generation of vines 287
6.14 Simulation from vines and truncated vine models 290
6.14.1 Simulation from vine copulas 291
6.14.2 Simulation from truncated vines and factor copulas 293
6.15 Partial correlations and vines 297
6.16 Partial correlations and factor structure 302
6.17 Searching for good truncated R-vine approximations 303
6.17.1 Greedy sequential approach using minimum spanning trees 305
6.17.2 Non-greedy algorithm 307
6.18 Summary for algorithms 308 7
7 Applications and data examples 309
7.1 Data analysis with misspecified copula models 309
7.1.1 Inference for dependence measures 310
7.1.2 Inference for tail-weighted dependence measures 313
7.2 Inferences on tail quantities 315
7.3 Discretized multivariate Gaussian and R-vine approximation 317
7.4 Insurance losses: bivariate continuous 319
7.5 Longitudinal count: multivariate discrete 322
7.6 Count time series 327
7.7 Multivariate extreme values 331
7.8 Multivariate financial returns 335
7.8.1 Copula-GARCH 335
7.8.2 Market returns 337
7.8.3 Stock returns over several sectors 342
7.9 Conservative tail inference 350
7.10 Item response: multivariate ordinal 353
7.11 SEIM model as vine: alienation data 355
xii CONTENTS
7.12 SEM model as vine: attitude-behavior data 359
7.13 Overview of applications 361
8 Theorems for properties of copulas 363
8.1 Absolutely continuous and singular components of multivariate distributions 363
8.2 Continuity properties of copulas 365
8.3 Dependence concepts 366
8.4 Frechet classes and compatibility 369
8.5 Archimedean copulas 374
8.6 Multivariate extreme value distributions 382
8.7 Mixtures of max-id distributions 386
8.8 Elliptical distributions 391
8.9 Tail dependence 394
8.10 Tail order 398
8.11 Combinatorics of vines 400
8.12 Vines and mixtures of conditional distributions 403
8.13 Factor copulas 410
8.14 Kendall functions 419
8.15 Laplace transforms 422
8.16 Regular variation 426
8.17 Summary for further reseach 427
A Laplace transforms and Archimedean generators 429
A.l Parametric Laplace transform families 429
A. 1.1 One-parameter LT families 429
A.1.2 Two-parameter LT families: group 1 431
A. 1.3 Two-parameter LT families: group 2 433
A. 1.4 LT families via integration 434
A.2 Archimedean generators in Nelsen’s book 435
Bibliography 437
*1
t
Index 459
|
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| language | English |
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| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Joe, Harry Verfasser (DE-588)1057991457 aut Dependence modeling with copulas Harry Joe Boca Raton, Fla. [u.a.] CRC Press 2015 XVIII, 462 S. graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 134 "A CRC title.". - Includes bibliographical references and index Copulas (Mathematical statistics) Dependence (Statistics) Probabilities Stochastische Abhängigkeit (DE-588)4220425-2 gnd rswk-swf Kopula Mathematik (DE-588)4529954-7 gnd rswk-swf Kopula Mathematik (DE-588)4529954-7 s Stochastische Abhängigkeit (DE-588)4220425-2 s DE-604 Monographs on statistics and applied probability 134 (DE-604)BV002494005 134 LoC Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027491062&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027491062&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Joe, Harry Dependence modeling with copulas Monographs on statistics and applied probability Copulas (Mathematical statistics) Dependence (Statistics) Probabilities Stochastische Abhängigkeit (DE-588)4220425-2 gnd Kopula Mathematik (DE-588)4529954-7 gnd |
| subject_GND | (DE-588)4220425-2 (DE-588)4529954-7 |
| title | Dependence modeling with copulas |
| title_auth | Dependence modeling with copulas |
| title_exact_search | Dependence modeling with copulas |
| title_full | Dependence modeling with copulas Harry Joe |
| title_fullStr | Dependence modeling with copulas Harry Joe |
| title_full_unstemmed | Dependence modeling with copulas Harry Joe |
| title_short | Dependence modeling with copulas |
| title_sort | dependence modeling with copulas |
| topic | Copulas (Mathematical statistics) Dependence (Statistics) Probabilities Stochastische Abhängigkeit (DE-588)4220425-2 gnd Kopula Mathematik (DE-588)4529954-7 gnd |
| topic_facet | Copulas (Mathematical statistics) Dependence (Statistics) Probabilities Stochastische Abhängigkeit Kopula Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027491062&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027491062&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002494005 |
| work_keys_str_mv | AT joeharry dependencemodelingwithcopulas |
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