Advances in mathematical and statistical modeling:
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| Format: | Book |
| Language: | English |
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Boston [u.a.]
Birkhäuser
2008
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| Series: | Statistics for industry and technology
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XXXIII, 368 S. Ill., graph. Darst. 26 cm |
| ISBN: | 9780817646257 9780817646264 |
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| 245 | 1 | 0 | |a Advances in mathematical and statistical modeling |c Barry C. Arnold ... ed. |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2008 | |
| 300 | |a XXXIII, 368 S. |b Ill., graph. Darst. |c 26 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 0 | |a Statistics for industry and technology | |
| 500 | |a Literaturangaben | ||
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| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Mathematical statistics |x Data processing |x Congresses | |
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| 700 | 1 | |a Arnold, Barry C. |d 1939- |0 (DE-588)111442435 |4 edt | |
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CONTENTS PREFACE XVII LIST OF CONTRIBUTORS XXI LIST OF TABLES XXVII LIST
OF FIGURES XXXI PART I DISTRIBUTION THEORY AND APPLICATIONS 1 ENRIQUE
CASTILLO'S CONTRIBUTIONS TO CONDITIONAL SPECIFICATION BARRY C ARNOLD 3
1.1 INTRODUCTION , 3 1.2 CONDITIONALS IN GIVEN EXPONENTIAL FAMILIES 4
1.3 CONDITIONALS IN GIVEN NON-EXPONENTIAL FAMILIES 8 1.4 TRINUTATED AND
WEIGHTED DISTRIBUTIONS 9 1.5 A DIGRESSION ON IMPROPER MODELS 9 L.FI
CHARAETEMATKNIS OF CLASSICAL MODELS VIA CONDITIONAL SPECIFICATIONS. 10
1.7 BACK TO THE BAYESIAN SCENARIO 10 1.8 INFERENCE FOR CONDITIONALLY
SPECIFIED MODELS 11 1.9 INCOMPLETE AND IMPRECISE CONDITIONAL
SPECIFICATION 11 1.10 FUTURE PROSPECTS 17 REFERENCES 17 2 THE POLYGONAL
DISTRIBUTION DIMURIS KARLIA AND, EVDOKIA XCKALAKI 21 2.1 INTRODUCTION 21
2.2 THE TRIANGULAR DISTRIBUTION 22 2.3 THE POLYGONAL DISTRIBUTION 23
2.3.1 ESTIMATION 25 2.4 THE POLYGONAL DISTRIBUTION AS A MIXING DENSITY
*. 26 2.4.1 TILT! BINOMIAL TRIANGULAR DISTRIBUTION 26 2.4.2 AN
APPLICATION 28 2.4.3 THE NEGATIVE BINOMIAL TRIANGULAR DISTRIBUTION 30
2.5 DISCUSSION 32 REFERENCOH 32 VIII CONTENTS 3 CONDITIONALLY SPECIFIED
MODELS: NEW DEVELOPMENTS AND APPLICATIONS JOSE MARIA SARABIA, MARIA
SARABIA, AND MARTA PASCUAL 35 3.1 INTRODUCTION 35 3.2 BIVARIATE POWER
CONDITIONALS DISTRIBUTION 36 3.2.1 BIVARIATE POISSON CONDITIONALS
DISTRIBUTION 36 3.2.2 BIVARIATE BINOMIAL CONDITIONALS DISTRIBUTION 37
3.2.3 A GENERAL CLASS 37 3.3 MIXTURE CONDITIONAL MODELS WITH
APPLICATIONS TO ACTUARIAL STATISTICS. 38 3.4 BIVARIATE INCOME
DISTRIBUTIONS 39 3.5 FLEXIBLE CONJUGATE PRIOR FAMILIES 39 3.5.1 HURDLE
COUNT DATA MODELS: BAYESIAN ANALYSIS 40 3.5.2 ESTIMATING WITH INCOMPLETE
COUNT DATA 40 3.6 CONDITIONAL HAZARD FUNCTIONS 41 REFERENCES 42 4
MODELLING OF INSURANCE CLAIM COUNT WITH HURDLE DISTRIBUTION FOR PANEL
DATA JEAN-PHILIPPE BOUCHER, MICHEL DENUIT T AND MONTSERRAT GUILLEN 45
4.1 INTRODUCTION 45 4.1.1 DATA USED 46 4.2 CROSS SECTION VERSUS PANEL
DATA 47 4.2.1 MODELLING 47 4.3 POISSON DISTRIBUTION 48 4.3.1 OVERVIEW 48
4.3.2 PANEL DATA 48 4.4 HURDLE MODELS 49 4.4.1 OVERVIEW 49 4.4.2 PANEL
DATA 52 4.5 PREDICTIVE DISTRIBUTION 53 4.5.1 POISSON 53 4.5.2 HURDLE 54
4.5.3 LINEAR CREDIBILITY 55 4.6 INSURANCE APPLICATION. 55 4.6.1
ESTIMATIONS 55 4.6.2 PREMIUMS 56 4.7 CONCLUSION 58 REFERENCES 58 5
DISTANCE-BASED ASSOCIATION AND MULTI-SAMPLE TESTS FOR GENERAL
MULTIVARIATE DATA CARLES M. CUADRAS 61 5.1 INTRODUCTION 61 5.2
MULTIVARIATE ASSOCIATION 62 5.2.1 EXAMPLE OF MULTIVARIATE ASSOCIATION 63
5.3 THE PROXIMITY FUNCTION 64 5.4 THE DISTANCE-BASED BAYES ALLOCATION
RULE 65 5.5 MULTIVARIATE MULTIPLE-SAMPLE TESTS 66 5.5.1 PARTITIONING THE
GEOMETRIC VARIABILITY , 66 CONTENTS IX 5.5.2 TESTS WII.LI PRINCIPAL
COORDINATES 07 5.5.'J TESTS WII.LI PROXIMITY FUNETIOIIH FJ8 R .H.* 1
MULTIVNRIUT.O DISPERSION (J ) 5.5.5 EXAMPLES OF NMLLKHIUNPLC! TESTS (IF)
REL'ERENCOH , 7() PART II PROBABILITY AND STATISTICS (I EMPIRICAL BAYES
ASSESSMENT OF THO HYPERPARAMETERS IN BAYESIAN FACTOR ANALYSIS *V. ,LAMC»
PITSH, KEY-11 SHIN, AND LEE. HUNT/ RUN 75 (I.L INTRODUCTION * , ., , 75
FI.2 THE HFA MODCIL 7FI (I.'I ASHCHHIH^, THE HY[)( I RPFVRAI[I(;1.(IRS
77 (I.'J. I A.SHCHSNX'NT OF AN , 77 (I.3.2 ASKIIKNIIICIIL, OF
NIIIIINIIIL \ 78 VTM.'.I AHHFSHINCIIT, OF H 78 ().'I.'I AHHIISHLLKMLT
OF /7 78 II.'A. 5 ITERATIVE CUIIIPUUI.TIOII OF THO LIYPORPA.NIIIKIT.OR.S
70 ().] HAYESIAU IWTIINNLIOII OF A, I \\L' 70 0.5 I'LXUINPJE 81 (I.(I
MCTLIOD ('OIIIJIARISON AND SUMMARY 84 RUFENUIET'H 85 PAR!; ILL ORDOR
STATLSTICK AND AIIALYNIA 7 NOGATIVO MIXTNRH, ORDOR STATIHTICH, AND
SYATEMH JTM/I' NTWURM MID I'RDRO J. HERNANDEZ 8!J 7.1 .INTRODUCTION 80
7.2 HDATION.SLIIPH BETWEEN MIXTUMS AND SY.STOMS 90 7.I'J I'ROIXFRLIT'H
OF MIXTURES AND SYSTEMS 92 7.4 TIN.' HRIDW STRNCL.UIC .' OF) API I (
NDIX 5)8 HCFCN^NCCH 90 8 MODOLH OF ORCUSRCUL DATA AND PRODUCTH OF BETA
RANDOM VARIABLES ERIC BRUTNTR TIN.D, LIDO KAMPX 1.01 8.1 INTMCLUEUUN ,
101 8.2 ITITCRUICDIATI! (JRDCI 1 8(.AL;I,STICS IMD UIT! OJ'DISROD
DIRICIIKIT DIHTRIHUTION . 1013 8, ( 'J PROPCRL,II!,S OF I'VAT^UONAL
ORDOR STATISTICW I(}5 ILT'ICRI'IU'CK 100 9 EXACT INFORONCO AND OPTIMAL
CENSORING SCHEME FOR A SIMPLE STCP-STREHH MODOL UNDER PROGRESSIVE
TYJ)E-II CENSORING QIHAN KIC, N. IHDAKRIXLMTM, AND JJONP-LTOON HAN 107
!.).L LUFRTIDIK'TIOU 107 0.2 MODEL DESCRIPTION MID MLKS 100 X CONTENTS
9.3 CONDITIONAL DISTRIBUTIONS OF THE MLES ILL 9.4 CONFIDENCE INTERVALS
117 9.4.1 EXACT CONFIDENCE INTERVALS 117 9.4.2 ASYMPTOTIC CONFIDENCE
INTERVALS 118 9.4.3 BOOTSTRAP CONFIDENCE INTERVALS 118 9.5 SIMULATION
STUDY 121 9.6 OPTIMAL CENSORING SCHEME 121 9.7 ILLUSTRATIVE EXAMPLES 123
9.8 CONCLUSIONS 125 APPENDIX: TABLES AND FIGURES 126 REFERENCES 136 PART
IV ENGINEERING MODELING 10 NON-GAUSSIAN STATE ESTIMATION IN POWER
SYSTEMS ROBERTO MMGUEZ, ANTONIO J. CONEJO, AND ALI S. HADI 141 10.1
INTRODUCTION 141 10.2 MAXIMUM LIKELIHOOD ESTIMATION 142 10.3
TRANSFORMATION OF RANDOM VARIABLES 143 10.3.1 ROSENBLATT TRANSFORMATION
144 10.3.2 NATAF TRANSFORMATION 144 10.3.3 ORTHOGONAL TRANSFORMATION OF
NORMAL RANDOM VARIABLES 145 10.4 THE TRANSFORMED LIKELIHOOD ESTIMATION
PROBLEM 146 10.5 GENERAL STATE ESTIMATION (GSE) FORMULATION 147 10.5.1
INDEPENDENT GAUSSIAN PROBABILITY DENSITY FUNCTION 147 10.5-2 DEPENDENT
GAUSSIAN PROBABILITY DENSITY FUNCTION 148 10.5.3 DEPENDENT NON-GAUSSIAN
PROBABILITY DENSITY FUNCTION 148 10.6 BAD DATA DETECTION 148 10.7
ILLUSTRATIVE EXAMPLE 148 10.7.1 STATISTICAL ASSUMPTIONS 149 10.8
CONCLUSIONS 154 REFERENCES 155 11 STATISTICS APPLIED TO WAVE CLIMATE ON
A BEACH PROFILE CARMEN CASTILLO AND CRISTINA SOLARES 157 11.1
INTRODUCTION * 157 11.2 OFFSHORE WAVE CLIMATE 158 11.3 LOCAL WAVE HEIGHT
DESCRIPTION 161 11.3.1 CONDITIONAL PROBABILITIES 161 11.3.2 ABSOLUTE
PROBABILITIES 163 11.4 CONSECUTIVE WAVE HEIGHTS 164 11.5 MAXIMUM WAVE
HEIGHT IQQ 11.5.1 CONDITIONAL PROBABILITIES 166 11.5.2 ABSOLUTE
PROBABILITIES 167 11.6 CONCLUSIONS 168 REFERENCES CONTENTS XI PART V
EXTREME VALUE THEORY 12 ON SOME DEPENDENCE MEASURES FOR MULTIVARIATE
EXTREME VALUE DISTRIBUTIONS ISHAY WEISSMAN 171 12.1 INTRODUCTION 171
12.2 DEPENDENCE COEFFICIENTS 172 12.3 EXAMPLES 174 12.4 RELATION BETWEEN
RJ AND T2 176 12.5 COMBINING TWO INDEPENDENT MODELS 179 REFERENCES 180
13 RATIO OF MAXIMUM, TO THE SUM FOR TESTING SUPER HEAVY TAILS CLAUDIA
NEVES AND ISABEL PRAGA ALVES 181 13.1 INTRODUCTION 181 13.2 MAIN RESULTS
183 13-3 SIMULATION RESULTS AND REAL DATA ANALYSIS 184 13.4 AUXILIARY
RESULTS 188 13-5 PROOFS 189 REFERENCES 193 14 TAIL BEHAVIOUR: AN
EMPIRICAL STUDY M. IVETTE GOMES, DINIS PESTANA, LIGIA RODRIGUES, AND
CLARA VISEU 195 14.1 INTRODUCTION 195 14.2 ASYMPTOTIC CPS FOR THE TAIL
INDEX AND THE VAR 197 14.3 REDUCED BIAS TAIL INDEX AND QUANTILE
ESTIMATORS 198 14.3.1 TAIL INDEX ESTIMATION 198 14.3.2 ASYMPTOTIC CI'S
FOR 7 BASED ON SECOND ORDER REDUCED-BIAS TAIL INDEX ESTIMATION 199
14.3.3 ADAPTIVE CHOICE OF THE LEVEL FOR REDUCED-BIAS ESTIMATORS 199
14.3.4 EXTREME QUANTILE OR VAR ESTIMATIO N 200 14.3.5 ASYMPTOTIC CI'S
FOR VAR P ON THE BASIS OF REDUCED-BIAS ESTIMATORS 200 14.4 AN ALGORITHM
FOR SEMI-PARAMETRIC TAIL ESTIMATION 200 14.5 THE USE OF A PARAMETRIC
QUANTILE METHOD IN TAIL INDEX AND QUANTILE ESTIMATION 201 14.6 FINANCIAL
DATA ANALYSIS 203 14.6.1 SECOND ORDER PARAMETER ESTIMATION 203 14.6.2
TAIL INDEX AND VAR P ESTIMATION 203 14.6.3 GRAPHICAL ILLUSTRATION OF THE
ADAPTIVE THRESHOLD CHOICE FOR TAIL INDEX AND VAR ESTIMATION 204 14.6.4
THE USE OF A PERCENTILE METHOD IN QUANTILE ESTIMATION 205 REFERENCES -
206 15 AN EXAMPLE OF REAL-LIFE DATA WHERE THE HILL ESTIMATOR IS CORRECT
ROLF-DIETER REISS AND ULF CORMANN 209 15.1 INTRODUCTION 209 15.2 THE
PARETO MODELING 210 XII CONTENTS 15.3 THE HILL ESTIMATOR 211 15.4
MODIFIED PICKANDS ESTIMATORS 212 15.5 ANALYZING THE LONG TERM COPEPOD
DATA 213 15.5.1 THE DATA SET 213 15.5.2 PARAMETRIC ESTIMATES FOR THE
COPEPOD DATA 213 15.5.3 MEDIAN EXCESS FUNCTIONS 214 15.6 COMPUTATIONAL
ASPECTS 215 REFERENCES 215 PART VI BUSINESS AND ECONOMICS APPLICATIONS
16 DERIVING CREDIBILITY PREMIUMS UNDE R DIFFERENT BAYESIAN METHODOLOGY
EMILIO GOMEZ DENIZ - 219 16.1 INTRODUCTION 219 16.2 CLASSICAL MODEL OF
BIIHLMANN 221 16.3 STANDARD BAYESIAN CREDIBILITY 222 16.4 CREDIBILITY
BASED ON ROBUST BAYESIAN ANALYSIS 223 16.5 BEYOND THE LOSS FUNCTION 226
16.6 DISCUSSION 228 REFERENCES 228 17 THE INFLUENCE OF TRANSPORT LINKS
ON DISAGGREGATION AND REGIONALIZATION METHODS IN INTERREGIONAL
INPUT-OUTPUT MODELS BETWEEN METROPOLITAN AND REMOTE AREAS FERNANDO
ESCOBEDO AND JOSE M. URENA 231 17.1 INTRODUCTION 231 17.2 METHODOLOGY
232 17.3 RESULTS AND DISCUSSION 236 17.4 CONCLUSIONS 240 REFERENCES 240
PART VII STATISTICAL METHODS 18 JACKKNIFE BIAS CORRECTION OF A CLOCK
OFFSET ESTIMATOR DANIEL R. JESKE 245 18.1 INTRODUCTION 245 18.2
CANDIDATE CLOCK OFFSET ESTIMATORS 247 18.2.1 PAXSON'S ESTIMATOR , , 247
18.2.2 BOOTSTRAP BIAS-CORRECTION 247 18.2.3 JACKKNIFE BIAS-CORRECTION
248 18.3 MEAN SQUARED ERROR UNDER EXPONENTIAL AND PARETO DISTRIBUTIONS
. 248 18.3.1 EXPONENTIAL DISTRIBUTION 248 18.3.2 PARETO DISTRIBUTION
249 18.4 ADDITIONAL MEAN SQUARED ERROR COMPARISONS VIA SIMULATION 250
18.4.1 LOGNORMAL, GAMMA AND WEIBULL DISTRIBUTION 250 18.4.2 HEAVY TAILED
DISTRIBUTIONS 252 CONTENTS XIII 18.5 SUMMARY 253 REFERENCES 254 19
PRETESTING IN POLYTOMOUS LOGISTIC REGRESSION MODELS BASED ON
PHI-DIVERGENCE MEASURES LEANDRO PARDO, MARIA LUISA MENENDEZ, AND NIRIAN
MARTIN 255 19.1 INTRODUCTION 255 19.2 PRELIMINARIES AND NOTATION 257
19.3 CONTIGUOUS ALTERNATIVE HYPOTHESES 259 19.4 ASYMPTOTIC
DISTRIBUTIONAL QUADRATIC RISK OF J§^ 3 , 3^ AND 3J^ 2 262 19.5
COMPARISON OF FI CH , (3^ AND ^ LT4 A 264 REFERENCES 265 20 A UNIFIED
APPROACH TO MODEL SELECTION, DISCRIMINATION, GOODNESS OF FIT AND
OUTLIERS IN TIME SERIES DANIEL PENA AND PEDRO GALEANO 267 20.1
INTRODUCTION 267 20.2 ESTIMATING ARMA TIME SERIES MODELS 268 20.3
QUADRATIC DISCRIMINATION OF ARMA TIME SERIES MODELS 269 20.4 GOODNESS OF
FIT FOR ARMA TIME SERIES MODELS 271 20.5 OUTLIERS IN ARMA TIME SERIES
MODELS 273 REFERENCES 277 21 GENERALIZED LINEAR MODELS DIAGNOSTICS FOR
BINARY DATA USING DIVERGENCE MEASURES J. A, PARDO AND M. C. PARDO 279
21.1 INTRODUCTION 279 21.2 CHECKING GOODNESS-OF-FIT 281 21.3 SIMULATION
STUDY 283 21.4 "OUTLYING" DETECTION PROCEDURES 285 REFERENCES 288 PART
VIII APPLIED MATHEMATICS 22 SOME PROBLEMS IN GEOMETRIC PROCESSING OF
SURFACES JAIME PUIG-PEY, AKEMI GDLVEZ, ANDRES IGLESIAS, PEDRO CORCUERA,
AND JOSE RODRIGUEZ 293 22.1 INTRODUCTION 293 22.2 MATHEMATICAL
PRELIMINARIES 294 22.3 HELICAL CURVES ON SURFACES 296 22.3.1 IMPLICIT
SURFACES 297 22.3.2 PARAMETRIC SURFACES 297 22.4 SILHOUETTE CURVE ON A
SURFACE 299 22.4.1 SURFACE IN IMPLICIT FORM 299 22.4.2 SURFACES IN
PARAMETRIC FORM 301 22.5 CONCLUSIONS AND FURTHER REMARKS 302 REFERENCES
303 XIV CONTENTS 23 GENERALIZED INVERSE COMPUTATION BASED ON AN
ORTHOGONAL DECOMPOSITION METHODOLOGY PATRICIA GOMEZ, BEATRIZ LACRUZ, AND
ROSA EVA PRUNEDA 305 23.1 INTRODUCTION 305 23.2 GENERALIZED INVERSE 306
23.3 THE ALGORITHM TO OBTAIN A GENERALIZED INVERSE 307 23.4 GENERALIZED
INVERSE UPDATING ALGORITHM 309 23.5 LEAST SQUARES ESTIMATION FOR LESS
THAN FULL RANK MODELS 312 23.6 CONCLUSIONS 315 REFERENCES , 315 24
SINGLE AND ENSEMBLE FAULT CLASSIFIERS BASED ON FEATURES SELECTED BY
MULTI-OBJECTIVE GENETIC ALGORITHMS ENRICO ZIO, PIERO BARALDI, GIULIO
GOLAM, AND NICOLA PEDRONI 317 24.1 INTRODUCTION 317 24.2 FEATURE
SELECTION FOR PATTERN CLASSIFICATION 318 24.2.1 AN OVERVIEW OF FEATURE
SELECTION TECHNIQUES 319 24.3 GA-BASED FEATURE SELECTION FOR PATTERN
CLASSIFICATION 320 24.4 CLASSIFICATION OF TRANSIENTS IN THE FEEDWATER
SYSTEM OF A BOILING WATER REACTOR 322 24.5 THE ENSEMBLE APPROACH TO
PATTERN CLASSIFICATION 323 24.5.1 THE CONSTRUCTION OF THE ENSEMBLE 323
24.5.2 INTEGRATION OF CLASS ASSIGNMENTS 324 24.6 APPLICATION TO MULTIPLE
FAULT CLASSIFICATION 326 24.7 CONCLUSIONS 327 REFERENCES 328 25
FEASIBILITY CONDITIONS IN ENGINEERING PROBLEMS INVOLVING A PARAMETRIC
SYSTEM OF LINEAR INEQUALITIES CRISTINA SOLARES AND EDUARDO W. V. CHAVES
331 25.1 INTRODUCTION 331 25.2 THE HEAT TRANSFER PROBLEM 332 25.3 A
FRACTURE MECHANICAL PROBLEM 335 25.4 THE BEAM PROBLEM 336 25.5
CONCLUSIONS 340 REFERENCES , 340 26 FORECASTING NONLINEAR SYSTEMS WITH
NEURAL NETWORKS VIA ANTICIPATED SYNCHRONIZATION SIXTO HERRERA, DANIEL
SAN-MARTIN, ANTONIO S. COFIFIO, AND JOSE M. GUTIERREZ 341 26.1
INTRODUCTION 341 26-2 ANTICIPATED SYNCHRONIZATION 342 26.3 NONLINEAR
TIME SERIES MODELING WITH NEURAL NETWORKS 345 26.4 ERROR GROWTH IN
SYNCHRONIZED CHAINS 347 26.5 CONCLUSIONS 349 REFERENCES , 349 CONTENTS
XV PART IX DISCRETE DISTRIBUTIONS 27 THE DISCRETE HALF-NORMAL
DISTRIBUTION ADRIENNE W. KEMP 353 27.1 INTRODUCTION 353 27.2 THE MAXIMUM
ENTROPY DERIVATION 354 27.3 THE LIMITING G-HYPER-POISSON-I DERIVATION
355 27.4 THE MORSE M/M/L QUEUE WITH BALKING 355 27.5 SUCCESS RUN
PROCESSES 356 27.6 MIXED HEINE DISTRIBUTION 357 27.7 PROPERTIES 358
REFERENCES 359 28 PARAMETER ESTIMATION FOR CERTAIN Q-HYPERGEOMETRIC
DISTRIBUTIONS DAVID KEMP 361 28.1 INTRODUCTION 361 28.2 SPECIAL CASES
AND PROPERTIES 362 28.3 ESTIMATION 364 REFERENCES 365 INDEX 367 |
| adam_txt |
CONTENTS PREFACE XVII LIST OF CONTRIBUTORS XXI LIST OF TABLES XXVII LIST
OF FIGURES XXXI PART I DISTRIBUTION THEORY AND APPLICATIONS 1 ENRIQUE
CASTILLO'S CONTRIBUTIONS TO CONDITIONAL SPECIFICATION BARRY C ARNOLD 3
1.1 INTRODUCTION , 3 1.2 CONDITIONALS IN GIVEN EXPONENTIAL FAMILIES 4
1.3 CONDITIONALS IN GIVEN NON-EXPONENTIAL FAMILIES 8 1.4 TRINUTATED AND
WEIGHTED DISTRIBUTIONS 9 1.5 A DIGRESSION ON IMPROPER MODELS 9 L.FI
CHARAETEMATKNIS OF CLASSICAL MODELS VIA CONDITIONAL SPECIFICATIONS. 10
1.7 BACK TO THE BAYESIAN SCENARIO 10 1.8 INFERENCE FOR CONDITIONALLY
SPECIFIED MODELS 11 1.9 INCOMPLETE AND IMPRECISE CONDITIONAL
SPECIFICATION 11 1.10 FUTURE PROSPECTS 17 REFERENCES 17 2 THE POLYGONAL
DISTRIBUTION DIMURIS KARLIA AND, EVDOKIA XCKALAKI 21 2.1 INTRODUCTION 21
2.2 THE TRIANGULAR DISTRIBUTION 22 2.3 THE POLYGONAL DISTRIBUTION 23
2.3.1 ESTIMATION 25 2.4 THE POLYGONAL DISTRIBUTION AS A MIXING DENSITY
*. 26 2.4.1 TILT! BINOMIAL TRIANGULAR DISTRIBUTION 26 2.4.2 AN
APPLICATION 28 2.4.3 THE NEGATIVE BINOMIAL TRIANGULAR DISTRIBUTION 30
2.5 DISCUSSION 32 REFERENCOH 32 VIII CONTENTS 3 CONDITIONALLY SPECIFIED
MODELS: NEW DEVELOPMENTS AND APPLICATIONS JOSE MARIA SARABIA, MARIA
SARABIA, AND MARTA PASCUAL 35 3.1 INTRODUCTION 35 3.2 BIVARIATE POWER
CONDITIONALS DISTRIBUTION 36 3.2.1 BIVARIATE POISSON CONDITIONALS
DISTRIBUTION 36 3.2.2 BIVARIATE BINOMIAL CONDITIONALS DISTRIBUTION 37
3.2.3 A GENERAL CLASS 37 3.3 MIXTURE CONDITIONAL MODELS WITH
APPLICATIONS TO ACTUARIAL STATISTICS. 38 3.4 BIVARIATE INCOME
DISTRIBUTIONS 39 3.5 FLEXIBLE CONJUGATE PRIOR FAMILIES 39 3.5.1 HURDLE
COUNT DATA MODELS: BAYESIAN ANALYSIS 40 3.5.2 ESTIMATING WITH INCOMPLETE
COUNT DATA 40 3.6 CONDITIONAL HAZARD FUNCTIONS 41 REFERENCES 42 4
MODELLING OF INSURANCE CLAIM COUNT WITH HURDLE DISTRIBUTION FOR PANEL
DATA JEAN-PHILIPPE BOUCHER, MICHEL DENUIT T AND MONTSERRAT GUILLEN 45
4.1 INTRODUCTION 45 4.1.1 DATA USED 46 4.2 CROSS SECTION VERSUS PANEL
DATA 47 4.2.1 MODELLING 47 4.3 POISSON DISTRIBUTION 48 4.3.1 OVERVIEW 48
4.3.2 PANEL DATA 48 4.4 HURDLE MODELS 49 4.4.1 OVERVIEW 49 4.4.2 PANEL
DATA 52 4.5 PREDICTIVE DISTRIBUTION 53 4.5.1 POISSON 53 4.5.2 HURDLE 54
4.5.3 LINEAR CREDIBILITY 55 4.6 INSURANCE APPLICATION. 55 4.6.1
ESTIMATIONS 55 4.6.2 PREMIUMS 56 4.7 CONCLUSION 58 REFERENCES 58 5
DISTANCE-BASED ASSOCIATION AND MULTI-SAMPLE TESTS FOR GENERAL
MULTIVARIATE DATA CARLES M. CUADRAS 61 5.1 INTRODUCTION 61 5.2
MULTIVARIATE ASSOCIATION 62 5.2.1 EXAMPLE OF MULTIVARIATE ASSOCIATION 63
5.3 THE PROXIMITY FUNCTION 64 5.4 THE DISTANCE-BASED BAYES ALLOCATION
RULE 65 5.5 MULTIVARIATE MULTIPLE-SAMPLE TESTS 66 5.5.1 PARTITIONING THE
GEOMETRIC VARIABILITY , 66 CONTENTS IX 5.5.2 TESTS WII.LI PRINCIPAL
COORDINATES 07 5.5.'J TESTS WII.LI PROXIMITY FUNETIOIIH FJ8 R .H.* 1
MULTIVNRIUT.O DISPERSION (J ) 5.5.5 EXAMPLES OF NMLLKHIUNPLC! TESTS (IF)
REL'ERENCOH , 7() PART II PROBABILITY AND STATISTICS (I EMPIRICAL BAYES
ASSESSMENT OF THO HYPERPARAMETERS IN BAYESIAN FACTOR ANALYSIS *V. ,LAMC»
PITSH, KEY-11 SHIN, AND LEE. HUNT/ RUN 75 (I.L INTRODUCTION * , ., , 75
FI.2 THE HFA MODCIL 7FI (I.'I ASHCHHIH^, THE HY[)( I RPFVRAI[I(;1.(IRS
77 (I.'J. I A.SHCHSNX'NT OF AN , 77 (I.3.2 ASKIIKNIIICIIL, OF
NIIIIINIIIL \ 78 VTM.'.I AHHFSHINCIIT, OF H 78 ().'I.'I AHHIISHLLKMLT
OF /7 78 II.'A. 5 ITERATIVE CUIIIPUUI.TIOII OF THO LIYPORPA.NIIIKIT.OR.S
70 ().] HAYESIAU IWTIINNLIOII OF A, I \\L' 70 0.5 I'LXUINPJE 81 (I.(I
MCTLIOD ('OIIIJIARISON AND SUMMARY 84 RUFENUIET'H 85 PAR!; ILL ORDOR
STATLSTICK AND AIIALYNIA 7 NOGATIVO MIXTNRH, ORDOR STATIHTICH, AND
SYATEMH JTM/I' NTWURM MID I'RDRO J. HERNANDEZ 8!J 7.1 .INTRODUCTION 80
7.2 HDATION.SLIIPH BETWEEN MIXTUMS AND SY.STOMS 90 7.I'J I'ROIXFRLIT'H
OF MIXTURES AND SYSTEMS 92 7.4 TIN.' HRIDW STRNCL.UIC .' OF) API I (
NDIX 5)8 HCFCN^NCCH 90 8 MODOLH OF ORCUSRCUL DATA AND PRODUCTH OF BETA
RANDOM VARIABLES ERIC BRUTNTR TIN.D, LIDO KAMPX 1.01 8.1 INTMCLUEUUN ,
101 8.2 ITITCRUICDIATI! (JRDCI 1 8(.AL;I,STICS IMD UIT! OJ'DISROD
DIRICIIKIT DIHTRIHUTION . 1013 8, ( 'J PROPCRL,II!,S OF I'VAT^UONAL
ORDOR STATISTICW I(}5 ILT'ICRI'IU'CK 100 9 EXACT INFORONCO AND OPTIMAL
CENSORING SCHEME FOR A SIMPLE STCP-STREHH MODOL UNDER PROGRESSIVE
TYJ)E-II CENSORING QIHAN KIC, N. IHDAKRIXLMTM, AND JJONP-LTOON HAN 107
!.).L LUFRTIDIK'TIOU 107 0.2 MODEL DESCRIPTION MID MLKS 100 X CONTENTS
9.3 CONDITIONAL DISTRIBUTIONS OF THE MLES ILL 9.4 CONFIDENCE INTERVALS
117 9.4.1 EXACT CONFIDENCE INTERVALS 117 9.4.2 ASYMPTOTIC CONFIDENCE
INTERVALS 118 9.4.3 BOOTSTRAP CONFIDENCE INTERVALS 118 9.5 SIMULATION
STUDY 121 9.6 OPTIMAL CENSORING SCHEME 121 9.7 ILLUSTRATIVE EXAMPLES 123
9.8 CONCLUSIONS 125 APPENDIX: TABLES AND FIGURES 126 REFERENCES 136 PART
IV ENGINEERING MODELING 10 NON-GAUSSIAN STATE ESTIMATION IN POWER
SYSTEMS ROBERTO MMGUEZ, ANTONIO J. CONEJO, AND ALI S. HADI 141 10.1
INTRODUCTION 141 10.2 MAXIMUM LIKELIHOOD ESTIMATION 142 10.3
TRANSFORMATION OF RANDOM VARIABLES 143 10.3.1 ROSENBLATT TRANSFORMATION
144 10.3.2 NATAF TRANSFORMATION 144 10.3.3 ORTHOGONAL TRANSFORMATION OF
NORMAL RANDOM VARIABLES 145 10.4 THE TRANSFORMED LIKELIHOOD ESTIMATION
PROBLEM 146 10.5 GENERAL STATE ESTIMATION (GSE) FORMULATION 147 10.5.1
INDEPENDENT GAUSSIAN PROBABILITY DENSITY FUNCTION 147 10.5-2 DEPENDENT
GAUSSIAN PROBABILITY DENSITY FUNCTION 148 10.5.3 DEPENDENT NON-GAUSSIAN
PROBABILITY DENSITY FUNCTION 148 10.6 BAD DATA DETECTION 148 10.7
ILLUSTRATIVE EXAMPLE 148 10.7.1 STATISTICAL ASSUMPTIONS 149 10.8
CONCLUSIONS 154 REFERENCES 155 11 STATISTICS APPLIED TO WAVE CLIMATE ON
A BEACH PROFILE CARMEN CASTILLO AND CRISTINA SOLARES 157 11.1
INTRODUCTION * 157 11.2 OFFSHORE WAVE CLIMATE 158 11.3 LOCAL WAVE HEIGHT
DESCRIPTION 161 11.3.1 CONDITIONAL PROBABILITIES 161 11.3.2 ABSOLUTE
PROBABILITIES 163 11.4 CONSECUTIVE WAVE HEIGHTS 164 11.5 MAXIMUM WAVE
HEIGHT IQQ 11.5.1 CONDITIONAL PROBABILITIES 166 11.5.2 ABSOLUTE
PROBABILITIES 167 11.6 CONCLUSIONS 168 REFERENCES CONTENTS XI PART V
EXTREME VALUE THEORY 12 ON SOME DEPENDENCE MEASURES FOR MULTIVARIATE
EXTREME VALUE DISTRIBUTIONS ISHAY WEISSMAN 171 12.1 INTRODUCTION 171
12.2 DEPENDENCE COEFFICIENTS 172 12.3 EXAMPLES 174 12.4 RELATION BETWEEN
RJ AND T2 176 12.5 COMBINING TWO INDEPENDENT MODELS 179 REFERENCES 180
13 RATIO OF MAXIMUM, TO THE SUM FOR TESTING SUPER HEAVY TAILS CLAUDIA
NEVES AND ISABEL PRAGA ALVES 181 13.1 INTRODUCTION 181 13.2 MAIN RESULTS
183 13-3 SIMULATION RESULTS AND REAL DATA ANALYSIS 184 13.4 AUXILIARY
RESULTS 188 13-5 PROOFS 189 REFERENCES 193 14 TAIL BEHAVIOUR: AN
EMPIRICAL STUDY M. IVETTE GOMES, DINIS PESTANA, LIGIA RODRIGUES, AND
CLARA VISEU 195 14.1 INTRODUCTION 195 14.2 ASYMPTOTIC CPS FOR THE TAIL
INDEX AND THE VAR 197 14.3 REDUCED BIAS TAIL INDEX AND QUANTILE
ESTIMATORS 198 14.3.1 TAIL INDEX ESTIMATION 198 14.3.2 ASYMPTOTIC CI'S
FOR 7 BASED ON SECOND ORDER REDUCED-BIAS TAIL INDEX ESTIMATION 199
14.3.3 ADAPTIVE CHOICE OF THE LEVEL FOR REDUCED-BIAS ESTIMATORS 199
14.3.4 EXTREME QUANTILE OR VAR ESTIMATIO N 200 14.3.5 ASYMPTOTIC CI'S
FOR VAR P ON THE BASIS OF REDUCED-BIAS ESTIMATORS 200 14.4 AN ALGORITHM
FOR SEMI-PARAMETRIC TAIL ESTIMATION 200 14.5 THE USE OF A PARAMETRIC
QUANTILE METHOD IN TAIL INDEX AND QUANTILE ESTIMATION 201 14.6 FINANCIAL
DATA ANALYSIS 203 14.6.1 SECOND ORDER PARAMETER ESTIMATION 203 14.6.2
TAIL INDEX AND VAR P ESTIMATION 203 14.6.3 GRAPHICAL ILLUSTRATION OF THE
ADAPTIVE THRESHOLD CHOICE FOR TAIL INDEX AND VAR ESTIMATION 204 14.6.4
THE USE OF A PERCENTILE METHOD IN QUANTILE ESTIMATION 205 REFERENCES -
206 15 AN EXAMPLE OF REAL-LIFE DATA WHERE THE HILL ESTIMATOR IS CORRECT
ROLF-DIETER REISS AND ULF CORMANN 209 15.1 INTRODUCTION 209 15.2 THE
PARETO MODELING 210 XII CONTENTS 15.3 THE HILL ESTIMATOR 211 15.4
MODIFIED PICKANDS ESTIMATORS 212 15.5 ANALYZING THE LONG TERM COPEPOD
DATA 213 15.5.1 THE DATA SET 213 15.5.2 PARAMETRIC ESTIMATES FOR THE
COPEPOD DATA 213 15.5.3 MEDIAN EXCESS FUNCTIONS 214 15.6 COMPUTATIONAL
ASPECTS 215 REFERENCES 215 PART VI BUSINESS AND ECONOMICS APPLICATIONS
16 DERIVING CREDIBILITY PREMIUMS UNDE R DIFFERENT BAYESIAN METHODOLOGY
EMILIO GOMEZ DENIZ - 219 16.1 INTRODUCTION 219 16.2 CLASSICAL MODEL OF
BIIHLMANN 221 16.3 STANDARD BAYESIAN CREDIBILITY 222 16.4 CREDIBILITY
BASED ON ROBUST BAYESIAN ANALYSIS 223 16.5 BEYOND THE LOSS FUNCTION 226
16.6 DISCUSSION 228 REFERENCES 228 17 THE INFLUENCE OF TRANSPORT LINKS
ON DISAGGREGATION AND REGIONALIZATION METHODS IN INTERREGIONAL
INPUT-OUTPUT MODELS BETWEEN METROPOLITAN AND REMOTE AREAS FERNANDO
ESCOBEDO AND JOSE M. URENA 231 17.1 INTRODUCTION 231 17.2 METHODOLOGY
232 17.3 RESULTS AND DISCUSSION 236 17.4 CONCLUSIONS 240 REFERENCES 240
PART VII STATISTICAL METHODS 18 JACKKNIFE BIAS CORRECTION OF A CLOCK
OFFSET ESTIMATOR DANIEL R. JESKE 245 18.1 INTRODUCTION 245 18.2
CANDIDATE CLOCK OFFSET ESTIMATORS 247 18.2.1 PAXSON'S ESTIMATOR , , 247
18.2.2 BOOTSTRAP BIAS-CORRECTION 247 18.2.3 JACKKNIFE BIAS-CORRECTION
248 18.3 MEAN SQUARED ERROR UNDER EXPONENTIAL AND PARETO DISTRIBUTIONS
. 248 18.3.1 EXPONENTIAL DISTRIBUTION 248 18.3.2 PARETO DISTRIBUTION
249 18.4 ADDITIONAL MEAN SQUARED ERROR COMPARISONS VIA SIMULATION 250
18.4.1 LOGNORMAL, GAMMA AND WEIBULL DISTRIBUTION 250 18.4.2 HEAVY TAILED
DISTRIBUTIONS 252 CONTENTS XIII 18.5 SUMMARY 253 REFERENCES 254 19
PRETESTING IN POLYTOMOUS LOGISTIC REGRESSION MODELS BASED ON
PHI-DIVERGENCE MEASURES LEANDRO PARDO, MARIA LUISA MENENDEZ, AND NIRIAN
MARTIN 255 19.1 INTRODUCTION 255 19.2 PRELIMINARIES AND NOTATION 257
19.3 CONTIGUOUS ALTERNATIVE HYPOTHESES 259 19.4 ASYMPTOTIC
DISTRIBUTIONAL QUADRATIC RISK OF J§^ 3 , 3^ AND 3J^ 2 262 19.5
COMPARISON OF FI CH , (3^ AND ^ LT4 A 264 REFERENCES 265 20 A UNIFIED
APPROACH TO MODEL SELECTION, DISCRIMINATION, GOODNESS OF FIT AND
OUTLIERS IN TIME SERIES DANIEL PENA AND PEDRO GALEANO 267 20.1
INTRODUCTION 267 20.2 ESTIMATING ARMA TIME SERIES MODELS 268 20.3
QUADRATIC DISCRIMINATION OF ARMA TIME SERIES MODELS 269 20.4 GOODNESS OF
FIT FOR ARMA TIME SERIES MODELS 271 20.5 OUTLIERS IN ARMA TIME SERIES
MODELS 273 REFERENCES 277 21 GENERALIZED LINEAR MODELS DIAGNOSTICS FOR
BINARY DATA USING DIVERGENCE MEASURES J. A, PARDO AND M. C. PARDO 279
21.1 INTRODUCTION 279 21.2 CHECKING GOODNESS-OF-FIT 281 21.3 SIMULATION
STUDY 283 21.4 "OUTLYING" DETECTION PROCEDURES 285 REFERENCES 288 PART
VIII APPLIED MATHEMATICS 22 SOME PROBLEMS IN GEOMETRIC PROCESSING OF
SURFACES JAIME PUIG-PEY, AKEMI GDLVEZ, ANDRES IGLESIAS, PEDRO CORCUERA,
AND JOSE RODRIGUEZ 293 22.1 INTRODUCTION 293 22.2 MATHEMATICAL
PRELIMINARIES 294 22.3 HELICAL CURVES ON SURFACES 296 22.3.1 IMPLICIT
SURFACES 297 22.3.2 PARAMETRIC SURFACES 297 22.4 SILHOUETTE CURVE ON A
SURFACE 299 22.4.1 SURFACE IN IMPLICIT FORM 299 22.4.2 SURFACES IN
PARAMETRIC FORM 301 22.5 CONCLUSIONS AND FURTHER REMARKS 302 REFERENCES
303 XIV CONTENTS 23 GENERALIZED INVERSE COMPUTATION BASED ON AN
ORTHOGONAL DECOMPOSITION METHODOLOGY PATRICIA GOMEZ, BEATRIZ LACRUZ, AND
ROSA EVA PRUNEDA 305 23.1 INTRODUCTION 305 23.2 GENERALIZED INVERSE 306
23.3 THE ALGORITHM TO OBTAIN A GENERALIZED INVERSE 307 23.4 GENERALIZED
INVERSE UPDATING ALGORITHM 309 23.5 LEAST SQUARES ESTIMATION FOR LESS
THAN FULL RANK MODELS 312 23.6 CONCLUSIONS 315 REFERENCES , 315 24
SINGLE AND ENSEMBLE FAULT CLASSIFIERS BASED ON FEATURES SELECTED BY
MULTI-OBJECTIVE GENETIC ALGORITHMS ENRICO ZIO, PIERO BARALDI, GIULIO
GOLAM, AND NICOLA PEDRONI 317 24.1 INTRODUCTION 317 24.2 FEATURE
SELECTION FOR PATTERN CLASSIFICATION 318 24.2.1 AN OVERVIEW OF FEATURE
SELECTION TECHNIQUES 319 24.3 GA-BASED FEATURE SELECTION FOR PATTERN
CLASSIFICATION 320 24.4 CLASSIFICATION OF TRANSIENTS IN THE FEEDWATER
SYSTEM OF A BOILING WATER REACTOR 322 24.5 THE ENSEMBLE APPROACH TO
PATTERN CLASSIFICATION 323 24.5.1 THE CONSTRUCTION OF THE ENSEMBLE 323
24.5.2 INTEGRATION OF CLASS ASSIGNMENTS 324 24.6 APPLICATION TO MULTIPLE
FAULT CLASSIFICATION 326 24.7 CONCLUSIONS 327 REFERENCES 328 25
FEASIBILITY CONDITIONS IN ENGINEERING PROBLEMS INVOLVING A PARAMETRIC
SYSTEM OF LINEAR INEQUALITIES CRISTINA SOLARES AND EDUARDO W. V. CHAVES
331 25.1 INTRODUCTION 331 25.2 THE HEAT TRANSFER PROBLEM 332 25.3 A
FRACTURE MECHANICAL PROBLEM 335 25.4 THE BEAM PROBLEM 336 25.5
CONCLUSIONS 340 REFERENCES , 340 26 FORECASTING NONLINEAR SYSTEMS WITH
NEURAL NETWORKS VIA ANTICIPATED SYNCHRONIZATION SIXTO HERRERA, DANIEL
SAN-MARTIN, ANTONIO S. COFIFIO, AND JOSE M. GUTIERREZ 341 26.1
INTRODUCTION 341 26-2 ANTICIPATED SYNCHRONIZATION 342 26.3 NONLINEAR
TIME SERIES MODELING WITH NEURAL NETWORKS 345 26.4 ERROR GROWTH IN
SYNCHRONIZED CHAINS 347 26.5 CONCLUSIONS 349 REFERENCES , 349 CONTENTS
XV PART IX DISCRETE DISTRIBUTIONS 27 THE DISCRETE HALF-NORMAL
DISTRIBUTION ADRIENNE W. KEMP 353 27.1 INTRODUCTION 353 27.2 THE MAXIMUM
ENTROPY DERIVATION 354 27.3 THE LIMITING G-HYPER-POISSON-I DERIVATION
355 27.4 THE MORSE M/M/L QUEUE WITH BALKING 355 27.5 SUCCESS RUN
PROCESSES 356 27.6 MIXED HEINE DISTRIBUTION 357 27.7 PROPERTIES 358
REFERENCES 359 28 PARAMETER ESTIMATION FOR CERTAIN Q-HYPERGEOMETRIC
DISTRIBUTIONS DAVID KEMP 361 28.1 INTRODUCTION 361 28.2 SPECIAL CASES
AND PROPERTIES 362 28.3 ESTIMATION 364 REFERENCES 365 INDEX 367 |
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| spelling | Advances in mathematical and statistical modeling Barry C. Arnold ... ed. Boston [u.a.] Birkhäuser 2008 XXXIII, 368 S. Ill., graph. Darst. 26 cm txt rdacontent n rdamedia nc rdacarrier Statistics for industry and technology Literaturangaben Statistische modellen gtt Datenverarbeitung Mathematical statistics Data processing Congresses Statistisches Modell (DE-588)4121722-6 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content (DE-588)1071861417 Konferenzschrift gnd-content Statistisches Modell (DE-588)4121722-6 s DE-604 Arnold, Barry C. 1939- (DE-588)111442435 edt http://d-nb.info/98346930X/04 Inhaltsverzeichnis SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016984031&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Advances in mathematical and statistical modeling Statistische modellen gtt Datenverarbeitung Mathematical statistics Data processing Congresses Statistisches Modell (DE-588)4121722-6 gnd |
| subject_GND | (DE-588)4121722-6 (DE-588)4143413-4 (DE-588)1071861417 |
| title | Advances in mathematical and statistical modeling |
| title_auth | Advances in mathematical and statistical modeling |
| title_exact_search | Advances in mathematical and statistical modeling |
| title_exact_search_txtP | Advances in mathematical and statistical modeling |
| title_full | Advances in mathematical and statistical modeling Barry C. Arnold ... ed. |
| title_fullStr | Advances in mathematical and statistical modeling Barry C. Arnold ... ed. |
| title_full_unstemmed | Advances in mathematical and statistical modeling Barry C. Arnold ... ed. |
| title_short | Advances in mathematical and statistical modeling |
| title_sort | advances in mathematical and statistical modeling |
| topic | Statistische modellen gtt Datenverarbeitung Mathematical statistics Data processing Congresses Statistisches Modell (DE-588)4121722-6 gnd |
| topic_facet | Statistische modellen Datenverarbeitung Mathematical statistics Data processing Congresses Statistisches Modell Aufsatzsammlung Konferenzschrift |
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