Confidence and prediction under covariates and prior information: = Konfidenz- und Prognoseintervalle unter Kovariaten und Vorinformation
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| Main Author: | |
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| Format: | Thesis Book |
| Language: | English |
| Published: |
Würzburg
2015
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| Subjects: | |
| Online Access: | Volltext Inhaltsverzeichnis |
| Physical Description: | xxviii, 261 Seiten Diagramme |
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Record in the Search Index
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| adam_text | CONFIDENCE
AND PREDICTION
UNDER
COVARIATES
AND
PRIOR INFORMATION
DISSERTATIONSSCLIRIFT ZTIR ERLANGIIIIG DES AKADEINISCHEN GRADES
EINES DOKTORS DER NATURWISSENSCHAFTEN
AN DER J ULIUS-MAXIMILIAIIS-UNIVERSITAT WIIRZBURG
VORGELEGT VON
KRISTINA LURZ
AUS BAMBERG
WIIRZBURG 2015
HTTP://D-NB.INFO/1081389729
CONTENTS
ABSTRACT III
LIST OF FIGURES X
LIST OF TABLES XII
1 INTRODUCTION 1
2 DESIGN AND ANALYSIS OF SHORTEST TWO-SIDED CONFIDENCE INTERVALS FOR A
PROBA
BILITY UNDER PRIOR INFORMATION 9
2.1 INTRODUCTION 9
2.2 PREDICTION REGIONS AND CONFIDENCE REGIONS 12
2.3 THE BETA PRIOR MODEL FOR INFERENCE ON A PROBABILITY P 16
2.4 PREDICTION LIKELIHOOD MAXIMISATION AND THE INTERVAL PROPERTY OF
CONFI
DENCE REGIONS FOR A PROBABILITY P 18
2.5 PROPERTIES OF WEIGHTS AND PREDICTION LIKELIHOOD RATIOS 19
2.6 PREDICTION INTERVALS AND CONFIDENCE INTERVALS FOR A PROBABILITY P 22
2.7 NUMERICAL COMPARISON WITH OTHER CONFIDENCE INTERVALS WITHOUT PRIOR
IN
FORMATION 25
2.8 NUMERICAL ANALYSIS OF THE EFFECT OF PRIOR INFORMATION 27
2.9 INDIFFERENCE PROBABILITY 32
2.9.1 DEFINITION AND MOUOTONICITY CHARACTERISTICS 32
2.9.2 NUMERICAL ANALYSIS OF THE INDIFFERENCE PROBABILITY 33
2.10 COMPUTATIONAL ALGORITHM 36
2.10.1 MAIN STEPS OF THE ALGORITHM 36
2.10.2 DETAILED DESCRIPTION OF THE ALGORITHM 37
2.10.3 COMPUTATIONAL CHALLENGES 41
2.11 CONCLUSION AND OUTLOOK 43
2.A APPENDIX 45
3 BAYESIAN CREDIBILITY INTERVALS FOR A PROBABILITY S3
3.1 INTRODUCTION 53
3.2 BAYESIAN CREDIBILITY INTERVALS 56
V
CONTENTS
3.3 BAYESIAN MEASUREMENT AND PREDICTION SPACES 58
3.4 HPD CREDIBILITY INTERVALS FOR A PROBABILITY 60
3.5 RELATION BETWEEN THE PROBABILITY CONTENT OF BAYESIAN HPD INTERVALS
AND
THE COVERAGE PROBABILITY 66
3.6 NUMERICAL COMPARISON OF BAYESIAN AND FRCQUENTIST MPS 68
3.7 ELICITING PRIOR INFORMATION 73
3.8 CONCLUSION AND OUTLOOK 78
3.A APPENDIX 82
4 MINIMUM VOLUME CONFIDENCE INTERVALS FOR THE POISSON PARAMETER UNDER
PRIOR
INFORMATION 91
4.1 INTRODUCTION 91
4.2 THE GAMMA PRIOR MODEL FOR INFERENCE ON THE POISSON PARAMETER 96
4.3 PREDICTION LIKELIHOOD MAXIMISATION AND THE INTERVAL PROPERTY OF
CONFI
DENCE REGIONS FOR THE POISSON PARAMETER 97
4.4 PROPERTIES OF WEIGHTS AND PREDICTION LIKELIHOOD RATIOS 98
4.5 PREDICTION INTERVALS AND CONFIDENCE INTERVALS FOR THE POISSOU
PARAMETER . 100
4.6 BAYESIAN CREDIBILITY INTERVALS FOR THE POISSON PARAMETER 104
4.7 COMPARISON WITH OTHER CONFIDENCE INTERVALS FOR THE POISSON PARAMETER
. . 109
4.8 NUMERICAL ANALYSIS OF THE MINIMUM VOLUME CONFIDENCE INTERVALS 110
4.9 CONCLUSION AND OUTLOOK 115
4.A APPENDIX 117
5 CONFIDENCE INTERVALS IN AUDIT POPULATIONS 125
5.1 INTRODUCTION 125
5.2 SAMPLING TECHNIQUES IN AUDITING 128
5.2.1 ATTRIBUTE SAMPLING 130
5.2.2 VARIABLE SAMPLING 131
5.2.3 MONETARY UNIT SAMPLING 132
5.2.4 COMBINED ATTRIBUTE AND VARIABLE SAMPLING 133
5.3 AUDIT POPULATIONS 134
5.4 THE STRINGER BOUND 135
5.5 TWO-SIDED STRINGER BOUNDS 137
5.5.1 DEFINITION 138
5.5.2 FINITE SAMPLE RESULTS 139
5.5.3 THE TWO-SIDED STRINGER BOUND IN DIFFERENT SCENARIOS 140
5.6 SIMULATION STUDY 146
CONTENTS
5.7 DEALING WITH BOTH UNDER- AND OVERSTATEMENT 154
5.8 CONCLUSION AND OUTLOOK 154
5.A APPENDIX 158
6 EXPONENTIAL SMOOTHING WITH COVARIATES WITH APPLICATION IN ELECTRICITY
LOAD
FORECASTING 159
6.1 INTRODUCTION 1 9
6.2 STATE-SPACE MODELS FOR EXPONENTIAL SMOOTHING WITH COVARIATES 160
6.3 SSOE MODELS FOR ESCOV UNDER MULTIPLE SEASONALITY 163
6.3.1 THE LINEAR SSOE MODEL 163
6.3.2 THE PARTIALLY LINEAR SSOE MODEL 169
6.4 EMPIRICAL FITTING OF ESCOV SSOE MODELS 171
6.5 THE LIKELIHOOD UNDER THE ESCOV SSOE MODEL 173
6.6 EMPIRICAL FORECASTING UNDER ESCOV SSOE MODELS 175
6.7 NON-CONSTANT COVARIATE COEFFICIENTS 177
6.8 RENORMALISATION OF SEASONAL PATTERNS 17!)
6.8.1 RENORMALISATION FOR ADDITIVE SEASONALITY 180
6.8.2 RENORMALISATION FOR MULTIPLICATIVE SEASONALITY 183
6.9 APPLICATION IN ELECTRICITY LOAD FORECASTING IN ITALY 186
6.9.1 INTRODUCTION TO THE LOAD FORECASTING STUDY 186
6.9.2 MODEL ESTIMATION FOR ELECTRICITY DEMAND TIME SERIES 189
6.9.3 RENORMALISATION OF ELECTRICITY LOAD SEASONALITIES 202
6.9.4 CONCLUSION OF THE LOAD FORECASTING STUDY 203
6.10 IMPLEMENTATION AND NUMERICAL ISSUES 204
6.10.1 PARAMETER OPTIMISATION 204
6.10.2 NOTATION AND COMPUTATION TIME 207
6.10.3 INITIAL STATES VALUES 208
6.11 CONCLUSION AND OUTLOOK 208
6.A APPENDIX 211
7 PREDICTION INTERVALS FOR EXPONENTIAL SMOOTHING WITH COVARIATES 225
7.1 INTRODUCTION 225
7.2 EMPIRICAL PREDICTION INTERVALS 228
7.2.1 PREDICTION INTERVALS BASED ON EMPIRICAL QUANTILES 228
7.2.2 NORMAL APPROXIMATION BASED PREDICTION INTERVALS 229
7.2.3 PREDICTION INTERVALS BASED ON CHEBYCHEV S INEQUALITY 230
7.2.4 PREDICTION INTERVALS BASED ON THE CAINP-MCIDELL INEQUALITY ....
232
VII
CONTENTS
7.3 BOOTSTRAP PREDICTION INTERVALS 233
7.4 MODEL-BASED PREDICTION INTERVALS OF PLUG-IN TYPE 235
7.5 PREDICTION INTERVALS BASED ON LINEAR EXPANSION OF THE ESCOV MODEL .
. . 237
7.5.1 LINEAR EXPANSION OF THE ESCOV MODEL 238
7.5.2 STATISTICAL ANALYSIS OF THE LINEAR EXPANSION OF THE ESCOV MODEL .
240
7.5.3 APPROXIMATE PREDICTION INTERVALS 241
7.6 SIMULATION STUDY BASED ON ELECTRICITY LOAD DATA 242
7.6.1 ITALIAN ELECTRICITY LOAD DATA 242
7.6.2 RESULTS OF THE SIMULATION STUDY 246
7.7 APPLICATION OF PREDICTION INTERVALS IN FORECASTING 247
7.8 CONCLUSION AND OUTLOOK 249
7.A APPENDIX 253
8 SUMMARY AND OUTLOOK 259
BIBLIOGRAPHY XXVIII
VIII
|
| any_adam_object | 1 |
| author | Lurz, Kristina |
| author_GND | (DE-588)1095669648 |
| author_facet | Lurz, Kristina |
| author_role | aut |
| author_sort | Lurz, Kristina |
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| dewey-full | 519.287 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.287 |
| dewey-search | 519.287 |
| dewey-sort | 3519.287 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| spelling | Lurz, Kristina Verfasser (DE-588)1095669648 aut Confidence and prediction under covariates and prior information = Konfidenz- und Prognoseintervalle unter Kovariaten und Vorinformation vorgelegt von Kristina Lurz aus Bamberg Konfidenz- und Prognoseintervalle unter Kovariaten und Vorinformation Würzburg 2015 xxviii, 261 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Dissertation Julius-Maximilians-Universität Würzburg 2015 Mit einer Zusammenfassung in deutscher Sprache Prognose (DE-588)4047390-9 gnd rswk-swf A-priori-Wissen (DE-588)4139159-7 gnd rswk-swf Konfidenzintervall (DE-588)4644801-9 gnd rswk-swf Binomialverteilung (DE-588)4145587-3 gnd rswk-swf Exponential smoothing (DE-588)4153384-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Binomialverteilung (DE-588)4145587-3 s Konfidenzintervall (DE-588)4644801-9 s Exponential smoothing (DE-588)4153384-7 s Prognose (DE-588)4047390-9 s A-priori-Wissen (DE-588)4139159-7 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:20-opus-122748 https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-122748 Resolving-System kostenfrei Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028838212&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lurz, Kristina Confidence and prediction under covariates and prior information = Konfidenz- und Prognoseintervalle unter Kovariaten und Vorinformation Prognose (DE-588)4047390-9 gnd A-priori-Wissen (DE-588)4139159-7 gnd Konfidenzintervall (DE-588)4644801-9 gnd Binomialverteilung (DE-588)4145587-3 gnd Exponential smoothing (DE-588)4153384-7 gnd |
| subject_GND | (DE-588)4047390-9 (DE-588)4139159-7 (DE-588)4644801-9 (DE-588)4145587-3 (DE-588)4153384-7 (DE-588)4113937-9 |
| title | Confidence and prediction under covariates and prior information = Konfidenz- und Prognoseintervalle unter Kovariaten und Vorinformation |
| title_alt | Konfidenz- und Prognoseintervalle unter Kovariaten und Vorinformation |
| title_auth | Confidence and prediction under covariates and prior information = Konfidenz- und Prognoseintervalle unter Kovariaten und Vorinformation |
| title_exact_search | Confidence and prediction under covariates and prior information = Konfidenz- und Prognoseintervalle unter Kovariaten und Vorinformation |
| title_full | Confidence and prediction under covariates and prior information = Konfidenz- und Prognoseintervalle unter Kovariaten und Vorinformation vorgelegt von Kristina Lurz aus Bamberg |
| title_fullStr | Confidence and prediction under covariates and prior information = Konfidenz- und Prognoseintervalle unter Kovariaten und Vorinformation vorgelegt von Kristina Lurz aus Bamberg |
| title_full_unstemmed | Confidence and prediction under covariates and prior information = Konfidenz- und Prognoseintervalle unter Kovariaten und Vorinformation vorgelegt von Kristina Lurz aus Bamberg |
| title_short | Confidence and prediction under covariates and prior information |
| title_sort | confidence and prediction under covariates and prior information konfidenz und prognoseintervalle unter kovariaten und vorinformation |
| title_sub | = Konfidenz- und Prognoseintervalle unter Kovariaten und Vorinformation |
| topic | Prognose (DE-588)4047390-9 gnd A-priori-Wissen (DE-588)4139159-7 gnd Konfidenzintervall (DE-588)4644801-9 gnd Binomialverteilung (DE-588)4145587-3 gnd Exponential smoothing (DE-588)4153384-7 gnd |
| topic_facet | Prognose A-priori-Wissen Konfidenzintervall Binomialverteilung Exponential smoothing Hochschulschrift |
| url | https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-122748 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028838212&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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