On the analysis of independencies in margins of a multivariate Distribution: = Zur Analyse von Unabhängigkeiten in den Rändern einer multivariaten Verteilung
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| Format: | Thesis Book |
| Language: | English |
| Published: |
1994
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | II, 93 S. Ill., graph. Darst. |
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| 245 | 1 | 0 | |a On the analysis of independencies in margins of a multivariate Distribution |b = Zur Analyse von Unabhängigkeiten in den Rändern einer multivariaten Verteilung |c vorgelegt von Göran Kauermann |
| 246 | 1 | 1 | |a Zur Analyse von Unabhängigkeiten in den Rändern einer multivariaten Verteilung |
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| adam_text | IMAGE 1
ON THE ANALYSIS OF INDEPENDENCIES
IN MARGINS OF A MULTIVARIATE DISTRIBUTION (ZUR ANALYSE VON
UNABHAENGIGKEITEN IN DEN RAENDERN EINER MULTIVARIATEN VERTEILUNG)
VORGELEGT VON
DIPLOM-WIRTSCHAFTSMATHEMATIKER GOERAN KAUERMANN AUS HAGEN
VOM FACHBEREICH 13 - INFORMATIK DER TECHNISCHEN UNIVERSITAET BERLIN ZUR
ERLANGUNG DES AKADEMISCHEN GRADES
DOKTOR DER NATURWISSENSCHAFTEN - DR. RER. NAT. -
GENEHMIGTE DISSERTATION
PROMOTIONSAUSSCHUSS:
VORSITZENDER: PROF. DR. GERHARD TUTZ BERICHTER: PROF. NANNY WERMUTH PH.
D. (UNIVERSITAET MAINZ) BERICHTER: PROF. DR. ULRICH KOCKELKORN
TAG DER WISSENSCHAFTLICHEN AUSSPRACHE: 20. JUNI 1994
BERLIN 1994
D 83
IMAGE 2
CONTENTS
0 INTRODUCTION 1
1 MULTIVARIATE NORMAL DISTRIBUTION 3
1.1 MOTIVATION 3
1.2 LINEAR STRUCTURAL EQUATION MODELS 9
1.2.1 THE MODEL 9
1.2.2 APPLICATION TO COVARIANCE GRAPHS 10
1.2.3 THE EM ALGORITHM 11
1.3 DUAL MAXIMUM LIKELIHOOD ESTIMATION 12
1.4 EXAMPLES 16
1.5 CONCLUSION 19
1.5.1 DISCUSSION 19
1.5.2 FURTHER MODELS 20
2 HIERARCHICAL LOG ODDS MODELS 21
2.1 MOTIVATION 21
2.2 HIERACHICAL LOG ODDS MODELS 23
2.2.1 DEFINITION 23
2.2.2 GENERAL DEFINITION 24
2.2.3 PROPERTIES 25
2.3 MAXIMUM LIKELIHOOD ESTIMATION 28
2.3.1 DERIVATION OF THE LIKELIHOOD EQUATION 28
2.3.2 ESTIMATION PROCEDURE 31
2.4 EXAMPLES 33
2.5 CONCLUSIONS 34
3 ANALYSIS OF INDEPENDENCIES BY AN EDGEWORTH EXPANSION 37
3.1 MOTIVATION 37
3.2 EXPANSION 39
3.3 ESTIMATION 44
3.4 EXAMPLE 47
3.5 CONCLUSION 48
I
IMAGE 3
11
A EXPONENTIAL FAMILIES 51
A.L INTRODUCTION 51
A.2 THE PRIMAL CUT 54
A.2.1 DEFINITION 54
A.2.2 PROPERTIES 56
A.2.3 EXAMPLES 58
A.3 ORTHOGONALITY 59
A.3.1 DEFINITION 59
A.3.2 ORTHOGONALITY IN EXPONENTIAL FAMILIES 60
A.4 DUAL LIKELIHOOD THEORY 62
A.4.1 MOTIVATION 62
A.4.2 THE DUAL CUT 63
A.4.3 ESTIMATION PRINCIPLES 65
A.5 THE DUAL CUT IN THE NORMAL DISTRIBUTION 67
A.6 EM ALGORITHM IN EXPONENTIAL FAMILIES 69
B E D G E W O R TH EXPANSION 71
B.L INTRODUCTION 71
B.2 DERIVATION OF THE FORMULAE 74
B.2.1 CUMULANT ESTIMATION 74
B.2.2 VARIANCE ESTIMATION 79
C GRAPH THEORETIC DEFINITIONS 85
D TECHNICAL PART 87
|
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| spelling | Kauermann, Göran Verfasser aut On the analysis of independencies in margins of a multivariate Distribution = Zur Analyse von Unabhängigkeiten in den Rändern einer multivariaten Verteilung vorgelegt von Göran Kauermann Zur Analyse von Unabhängigkeiten in den Rändern einer multivariaten Verteilung 1994 II, 93 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Berlin, Techn. Univ., Diss., 1994 Multivariate Normalverteilung (DE-588)4227589-1 gnd rswk-swf Maximum-Likelihood-Schätzung (DE-588)4194624-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Multivariate Normalverteilung (DE-588)4227589-1 s Maximum-Likelihood-Schätzung (DE-588)4194624-8 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006540941&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kauermann, Göran On the analysis of independencies in margins of a multivariate Distribution = Zur Analyse von Unabhängigkeiten in den Rändern einer multivariaten Verteilung Multivariate Normalverteilung (DE-588)4227589-1 gnd Maximum-Likelihood-Schätzung (DE-588)4194624-8 gnd |
| subject_GND | (DE-588)4227589-1 (DE-588)4194624-8 (DE-588)4113937-9 |
| title | On the analysis of independencies in margins of a multivariate Distribution = Zur Analyse von Unabhängigkeiten in den Rändern einer multivariaten Verteilung |
| title_alt | Zur Analyse von Unabhängigkeiten in den Rändern einer multivariaten Verteilung |
| title_auth | On the analysis of independencies in margins of a multivariate Distribution = Zur Analyse von Unabhängigkeiten in den Rändern einer multivariaten Verteilung |
| title_exact_search | On the analysis of independencies in margins of a multivariate Distribution = Zur Analyse von Unabhängigkeiten in den Rändern einer multivariaten Verteilung |
| title_full | On the analysis of independencies in margins of a multivariate Distribution = Zur Analyse von Unabhängigkeiten in den Rändern einer multivariaten Verteilung vorgelegt von Göran Kauermann |
| title_fullStr | On the analysis of independencies in margins of a multivariate Distribution = Zur Analyse von Unabhängigkeiten in den Rändern einer multivariaten Verteilung vorgelegt von Göran Kauermann |
| title_full_unstemmed | On the analysis of independencies in margins of a multivariate Distribution = Zur Analyse von Unabhängigkeiten in den Rändern einer multivariaten Verteilung vorgelegt von Göran Kauermann |
| title_short | On the analysis of independencies in margins of a multivariate Distribution |
| title_sort | on the analysis of independencies in margins of a multivariate distribution zur analyse von unabhangigkeiten in den randern einer multivariaten verteilung |
| title_sub | = Zur Analyse von Unabhängigkeiten in den Rändern einer multivariaten Verteilung |
| topic | Multivariate Normalverteilung (DE-588)4227589-1 gnd Maximum-Likelihood-Schätzung (DE-588)4194624-8 gnd |
| topic_facet | Multivariate Normalverteilung Maximum-Likelihood-Schätzung Hochschulschrift |
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