Improved estimation of distribution parameters: Stein-type estimators
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Stuttgart u.a.
Teubner
1992
|
| Series: | Teubner-Texte zur Mathematik
128 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zs.-Fassung in dt., engl., franz. und russ. Sprache. - Literaturverz. S. 154 - 167 |
| Physical Description: | 174 S. |
| ISBN: | 3815420288 |
Staff View
MARC
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| 100 | 1 | |a Hoffmann, Kurt |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Improved estimation of distribution parameters |b Stein-type estimators |c Kurt Hoffmann |
| 264 | 1 | |a Stuttgart u.a. |b Teubner |c 1992 | |
| 300 | |a 174 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Teubner-Texte zur Mathematik |v 128. | |
| 500 | |a Zs.-Fassung in dt., engl., franz. und russ. Sprache. - Literaturverz. S. 154 - 167 | ||
| 650 | 7 | |a Distribution (théorie des probabilités) |2 ram | |
| 650 | 4 | |a Estimateur James-Stein | |
| 650 | 4 | |a Estimation | |
| 650 | 4 | |a Famille exponentielle | |
| 650 | 4 | |a Variance minimum | |
| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 4 | |a Estimation theory | |
| 650 | 0 | 7 | |a Parameterschätzung |0 (DE-588)4044614-1 |2 gnd |9 rswk-swf |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
1. INTRODUCTION 6
1.1. INTRODUCTORY REMARKS 6
1.2. OUTLINE OF THE BOOK 9
2. STEIN TYPE ESTIMATORS OF THE MEANS
OF A MULTIVARIATE NORMAL DISTRIBUTION 11
2.1. A REPRESENTATION OF THE RISK DIFFERENCE 13
2.2. THE CLASSICAL JAMES STEIN ESTIMATOR AS IMPROVED
ESTIMATOR 16
2.3. A BAYESIAN APPROACH TO THE JAMES STEIN ESTIMATOR . . 23
2.4. THE POSITIVE PART JAMES STEIN ESTIMATOR 27
2.5. A CLASS OF ESTIMATORS THAT DOMINATE THE USUAL ONE. . . 30
2.6. IMPROVED ESTIMATORS WITH GOOD BAYES PROPERTIES ... 35
2.6.1. A GENERALIZED JAMES STEIN ESTIMATOR 35
2.6.2. A SMOOTHING MODIFICATION OF THE POSITIVE PART
ESTIMATORS 38
2.7. ADMISSIBLE IMPROVED ESTIMATORS HH
2.8. IMPROVED ESTIMATORS SHIFTING X TOWARDS SOME DATA BASED
POINT 53
2.9. THE CASE OF A GENERALIZED QUADRATIC RISK 55
2.10. THE ROBUSTNESS OF STEIN TYPE ESTIMATORS 56
2.11. THE CASE OF A MORE GENERAL COVARIANCE STRUCTURE . . 59
2.12. APPLICATION TO LINEAR REGRESSION 63
2.13. BIBLIOGRAPHICAL NOTES 65
3
3. IMPROVED ESTIMATION OF PARAMETERS
IN CONTINUOUS EXPONENTIAL FAMILIES 69
3.1. THE CASE OF A ONE PARAMETER CANONICAL EXPONENTIAL
FAMILY 71
3.1.1. PAIRS OF ESTIMATORS WITH POSITIVE RISK
DIFFERENCE 73
3.1.2. SUFFICIENT CONDITIONS FOR THE INADMISSIBILITY OF
ESTIMATORS 79
3.2. THE CASE OF A MULTIPARAMETER CANONICAL EXPONENTIAL
FAMILY 86
3.2.1. PAIRS OF ESTIMATORS WITH POSITIVE RISK
DIFFERENCE 87
3.2.2. A^SUPERHARMONIC FUNCTIONS 92
3.2.3. ESTIMATORS DOMINATING THE MINIMUM VARIANCE
UNBIASED ESTIMATOR 96
3.2.4. CONSTRUCTION OF IMPROVED ESTIMATORS
FOR A SUBCLASS OF INADMISSIBLE ESTIMATORS . . 104
3.3. GENERALIZATIONS TO NONCANONICAL EXPONENTIAL FAMILIES 109
3.4. BIBLIOGRAPHICAL NOTES 120
4. IMPROVED ESTIMATION OF PARAMETERS IN DISCRETE
EXPONENTIAL FAMILIES WITH UNBOUNDED SUPPORT . . 121
1.1. THE ADMISSIBILITY OF THE MINIMUM VARIANCE
UNBIASED ESTIMATOR IN THE UNIVARIATE CASE ... 122
4.2. ESTIMATORS DOMINATING THE MINIMUM VARIANCE UNBIASED
ESTIMATOR UNDER SQUARED ERROR LOSS IN THE MULTIVARATE CASE 129
4.3. IMPROVED ESTIMATORS UNDER NORMALIZED SQUARED ERROR
LOSS 134
4.4. THE PROBLEM OF IMPROVING NONSTANDARD ESTIMATORS . . 140
4.5. BIBLIOGRAPHICAL NOTES 1*2
4
5. APPENDIX 145
REFERENCES 154
AUTHOR INDEX 168
SUBJECT INDEX 172
NOTATIONAL CONVENTIONS . 174
5
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| id | DE-604.BV006605869 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:49:07Z |
| institution | BVB |
| isbn | 3815420288 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004219754 |
| oclc_num | 25646443 |
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| physical | 174 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Teubner |
| record_format | marc |
| series | Teubner-Texte zur Mathematik |
| series2 | Teubner-Texte zur Mathematik |
| spelling | Hoffmann, Kurt Verfasser aut Improved estimation of distribution parameters Stein-type estimators Kurt Hoffmann Stuttgart u.a. Teubner 1992 174 S. txt rdacontent n rdamedia nc rdacarrier Teubner-Texte zur Mathematik 128. Zs.-Fassung in dt., engl., franz. und russ. Sprache. - Literaturverz. S. 154 - 167 Distribution (théorie des probabilités) ram Estimateur James-Stein Estimation Famille exponentielle Variance minimum Distribution (Probability theory) Estimation theory Parameterschätzung (DE-588)4044614-1 gnd rswk-swf Parameterschätzung (DE-588)4044614-1 s DE-604 Teubner-Texte zur Mathematik 128 (DE-604)BV000012607 128 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004219754&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hoffmann, Kurt Improved estimation of distribution parameters Stein-type estimators Teubner-Texte zur Mathematik Distribution (théorie des probabilités) ram Estimateur James-Stein Estimation Famille exponentielle Variance minimum Distribution (Probability theory) Estimation theory Parameterschätzung (DE-588)4044614-1 gnd |
| subject_GND | (DE-588)4044614-1 |
| title | Improved estimation of distribution parameters Stein-type estimators |
| title_auth | Improved estimation of distribution parameters Stein-type estimators |
| title_exact_search | Improved estimation of distribution parameters Stein-type estimators |
| title_full | Improved estimation of distribution parameters Stein-type estimators Kurt Hoffmann |
| title_fullStr | Improved estimation of distribution parameters Stein-type estimators Kurt Hoffmann |
| title_full_unstemmed | Improved estimation of distribution parameters Stein-type estimators Kurt Hoffmann |
| title_short | Improved estimation of distribution parameters |
| title_sort | improved estimation of distribution parameters stein type estimators |
| title_sub | Stein-type estimators |
| topic | Distribution (théorie des probabilités) ram Estimateur James-Stein Estimation Famille exponentielle Variance minimum Distribution (Probability theory) Estimation theory Parameterschätzung (DE-588)4044614-1 gnd |
| topic_facet | Distribution (théorie des probabilités) Estimateur James-Stein Estimation Famille exponentielle Variance minimum Distribution (Probability theory) Estimation theory Parameterschätzung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004219754&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012607 |
| work_keys_str_mv | AT hoffmannkurt improvedestimationofdistributionparameterssteintypeestimators |