Exploiting continuity: maximum entropy estimation of continuous distributions
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, Mass.
Ballinger
1984
|
| Series: | Series on econometrics and management sciences
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 246 S. |
| ISBN: | 0088109852 0884109852 |
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MARC
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| 245 | 1 | 0 | |a Exploiting continuity |b maximum entropy estimation of continuous distributions |c Henri Theil ; Denzil G. Fiebig |
| 264 | 1 | |a Cambridge, Mass. |b Ballinger |c 1984 | |
| 300 | |a XV, 246 S. | ||
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Record in the Search Index
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| adam_text | Contents
List of Figures ix
List of Tables xi
Acknowledgments xv
Introduction 1
Chapter 1 — The Maximum Entropy Principle 5
1.1 Introduction 5
1.2 The Measurement of Information 6
1.3 The Entropy of a Continuous Distribution 8
1.4 Multivariate Extensions 10
1.5 Conditional Entropies and Average Conditional En¬
tropies 12
Chapter 2 — The ME Distribution of a Univariate Sample 15
2.1 Introduction 15
2.2 Mass and Mean Preserving Constraints 16
2.3 The Univariate ME Distribution 17
2.4 Derivations 20
v
vi
Chapter 3 — The ME Distribution of a Multivariate Sample 25
3.1 The Bivariate and Multivariate ME Distributions 25
3.2 Secondary Midpoints of a Bivariate Sample 28
3.3 The ME Covariance Matrix 30
3.4 The ME Variance Further Considered 31
3.5 A Numerical Example 34
3.6 The Expected Mutual Information of the ME Distri¬
bution 35
3.7 The ME Distribution with Missing Values 39
3.8 The ME Distribution with Ties 43
Chapter 4 — More on the Univariate ME Distribution:
Evidence and Extensions 47
4.1 The ME Median 47
4.2 The ME Quartiles and Interquartile Distance 49
4.3 Quantiles in the Tails 52
4.4 Higher Order Moments 56
4.5 The Symmetric ME Distribution 58
4.6 Outliers 71
4.7 Restricted ME Distributions 75
Chapter 5 — The ME Covariance Matrix: Evidence and
Extensions 79
5.1 Ridge and Shrinkage: The ME Variance under Normality 7 9
5.2 The ME Correlation Coefficient under Bivariate Nor¬
mality 81
5.3 A Risk Evaluation of the ME Covariance Matrix 87
5.4 Extensions to Missing Values and Empirical Bayes 90
5.5 The Hybrid Sample—ME Covariance Matrix 94
5.6 Regressions Based on Few Observations 99
5.7 Extension to Multiple Regression 108
Chapter 6 — Canonical Correlation Coefficients and Con¬
strained Regressions 111
6.1 How Asymptotic Tests Can Be Misleading 111
6.2 Canonical Correlations and Applications 113
6.3 Estimation of Canonical Correlations 118
6.4 Symmetry Constrained Estimation 124
6.5 Discussion of the Results 126
vii
Chapter 7 — Simultaneous Equation Estimation from
Undersized Samples 133
7.1 Introduction 133
7.2 The Problem of Undersized Samples 136
7.3 The Case of Two Variables 138
7.4 Extension to Three Variables 146
7.5 Further Extensions 150
Appendix A — Measures of Statistical Information Theory 151
Al An Axiomatic Approach to the Measurement of In¬
formation 151
A2 The Expected Information of a Nondefinitive Message 153
A3 Derivations 155
A4 Aggregation Properties of Informational Measures 156
A5 The Kullback—Leibler Mean Information 158
A6 Some Results for the Multivariate Normal Distribution 160
A7 The Measurement of Inequality 161
A8 Disutility Weighted Informational Measures 165
Appendix B — Derivations for the ME Distribution 169
Bl Univariate ME Moments and Cumulants 169
B2 Bivariate ME Moments and Cumulants 174
B3 More about Ties 178
B4 The Effects of Symmetrizing Order Statistics 181
B5 More about Outliers 185
B6 The Positive ME Distribution 192
Appendix C — Additional Simulation Evidence 195
Cl Two Different Ways of Symmetrizing a Distribution 195
C2 More on Correlation Estimation 196
C3 More on Symmetric Normal Mixtures 197
C4 More on Risk Evaluation of Covariance Matrices 208
Appendix D — Elements of Consumption Theory 219
Dl The Differential Approach to Consumption Theory 219
D2 The Rotterdam Model 224
D3 Working s Model and Extensions 224
viii
Appendix E — Computer Programs 229
El Discussion of Computational Aspects 229
E2 SAS and FORTRAN Programs 231
Bibliography 237
Index 243
About the Authors 247
|
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| id | DE-604.BV000228799 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:10:45Z |
| institution | BVB |
| isbn | 0088109852 0884109852 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000137010 |
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| physical | XV, 246 S. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Ballinger |
| record_format | marc |
| series | Series on econometrics and management sciences |
| series2 | Series on econometrics and management sciences |
| spelling | Theil, Henri 1924-2000 Verfasser (DE-588)123488400 aut Exploiting continuity maximum entropy estimation of continuous distributions Henri Theil ; Denzil G. Fiebig Cambridge, Mass. Ballinger 1984 XV, 246 S. txt rdacontent n rdamedia nc rdacarrier Series on econometrics and management sciences 1 Distribution (Théorie des probabilités) Distribution (théorie des probabilités) ram Estimation, Théorie de l' Estimation, théorie de l' ram Distribution (Probability theory) Estimation theory Maximum entropy method Schätztheorie (DE-588)4121608-8 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Verteilungstheorie (DE-588)4133628-8 gnd rswk-swf Verteilungstheorie (DE-588)4133628-8 s DE-604 Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s Schätztheorie (DE-588)4121608-8 s Fiebig, Denzil G. Verfasser (DE-588)170129217 aut Series on econometrics and management sciences 1 (DE-604)BV000896863 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000137010&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Theil, Henri 1924-2000 Fiebig, Denzil G. Exploiting continuity maximum entropy estimation of continuous distributions Series on econometrics and management sciences Distribution (Théorie des probabilités) Distribution (théorie des probabilités) ram Estimation, Théorie de l' Estimation, théorie de l' ram Distribution (Probability theory) Estimation theory Maximum entropy method Schätztheorie (DE-588)4121608-8 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Verteilungstheorie (DE-588)4133628-8 gnd |
| subject_GND | (DE-588)4121608-8 (DE-588)4121894-2 (DE-588)4133628-8 |
| title | Exploiting continuity maximum entropy estimation of continuous distributions |
| title_auth | Exploiting continuity maximum entropy estimation of continuous distributions |
| title_exact_search | Exploiting continuity maximum entropy estimation of continuous distributions |
| title_full | Exploiting continuity maximum entropy estimation of continuous distributions Henri Theil ; Denzil G. Fiebig |
| title_fullStr | Exploiting continuity maximum entropy estimation of continuous distributions Henri Theil ; Denzil G. Fiebig |
| title_full_unstemmed | Exploiting continuity maximum entropy estimation of continuous distributions Henri Theil ; Denzil G. Fiebig |
| title_short | Exploiting continuity |
| title_sort | exploiting continuity maximum entropy estimation of continuous distributions |
| title_sub | maximum entropy estimation of continuous distributions |
| topic | Distribution (Théorie des probabilités) Distribution (théorie des probabilités) ram Estimation, Théorie de l' Estimation, théorie de l' ram Distribution (Probability theory) Estimation theory Maximum entropy method Schätztheorie (DE-588)4121608-8 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd Verteilungstheorie (DE-588)4133628-8 gnd |
| topic_facet | Distribution (Théorie des probabilités) Distribution (théorie des probabilités) Estimation, Théorie de l' Estimation, théorie de l' Distribution (Probability theory) Estimation theory Maximum entropy method Schätztheorie Wahrscheinlichkeitsverteilung Verteilungstheorie |
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| volume_link | (DE-604)BV000896863 |
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