Non-regular statistical estimation:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1995
|
| Series: | Lecture notes in statistics
107 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 183 S. graph. Darst. |
| ISBN: | 0387945784 |
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Record in the Search Index
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| adam_text | MASAFUMI AKAHIRA KEI TAKEUCHI NON-REGULAR STATISTICAL ESTIMATION
SPRINGER CONTENTS CHAPTER 1. GENERAL DISCUSSIONS ON UNBIASED ESTIMATION
1 1.1. FORMULATION 1 1.2. UNDOMINATED CASE 3 1.3. THE SUPPORT DEPENDING
ON THE PARAMETER 5 1.4. DISCRETE PARAMETER SET 11 1.5. DISCONTINUOUS AND
NON-DIFFERENTIABLE DENSITY 13 1.6. NON SQUARE-INTEGRABLE LIKELIHOOD
RATIO 15 1.7. ASYMPTOTIC THEORY FOR NON-REGULAR CASES 16 1.8. ASYMPTOTIC
BAYES POSTERIOR DISTRIBUTION OF THE PARAMETER IN NON-REGULAR CASES 16
1.9. OVERVIEW 18 CHAPTER 2. LOWER BOUND FOR THE VARIANCE OF UNBIASED
ESTIMATORS . . 20 2.1. MINIMUM VARIANCE 20 2.2. BHATTACHARYYA TYPE BOUND
FOR THE VARIANCE OF UNBIASED ESTIMATORS IN NON-REGULAR CASES 25 2.3.
LOWER BOUND FOR THE VARIANCE OF UNBIASED ESTIMATORS FOR ONE-DIRECTIONAL
DISTRIBUTIONS 33 2.4. A SECOND TYPE OF ONE-DIRECTIONAL DISTRIBUTION AND
THE LOWER BOUND FOR THE VARIANCE OF UNBIASED ESTIMATORS . . . 44 2.5.
LOCALLY MINIMUM VARIANCE UNBIASED ESTIMATION 49 CHAPTER 3. AMOUNTS OF
INFORMATION AND THE MINIMUM VARIANCE UNBIASED ESTIMATION 61 3.1. FISHER
INFORMATION AND THE MINIMUM VARIANCE UNBIASED ESTIMATION 61 3.2.
EXAMPLES ON UNBIASED ESTIMATORS WITH ZERO VARIANCE . . . 63 3.3. A
DEFINITION OF THE GENERALIZED AMOUNT OF INFORMATION . . 65 3.4. EXAMPLES
ON THE GENERALIZED AMOUNT OF INFORMATION . . . 68 3.5. ORDER OF
CONSISTENCY 77 CHAPTER 4. LOSS OF INFORMATION ASSOCIATED WITH THE ORDER
STATISTICS AND RELATED ESTIMATORS IN THE CASE OF DOUBLE EXPONENTIAL
DISTRIBUTIONS 84 4.1. LOSS OF INFORMATION OF THE ORDER STATISTICS 84
4.2. THE ASYMPTOTIC LOSS OF INFORMATION 87 4.3. PROOFS OF THEOREMS IN
SECTION 4.2 91 4.4. DISCRETIZED LIKELIHOOD ESTIMATION 94 4.5. SECOND
ORDER ASYMPTOTIC COMPARISON OF THE DISCRETIZED LIKELIHOOD ESTIMATOR WITH
OTHERS 99 CHAPTER 5. ESTIMATION OF A COMMON PARAMETER FOR POOLED SAMPLES
FROM THE UNIFORM DISTRIBUTIONS AND THE DOUBLE EXPONENTIAL DISTRIBUTIONS
104 5.1. ESTIMATORS OF A COMMON PARAMETER FOR THE UNIFORM DISTRIBUTIONS
104 VIII 5.2. COMPARISON OF THE QUASI-MLE, THE WEIGHTED ESTIMATOR AND
OTHERS FOR THE UNIFORM DISTRIBUTIONS 107 5.3. ESTIMATORS OF A COMMON
PARAMETER FOR THE DOUBLE EXPONENTIAL DISTRIBUTIONS 113 5.4. SECOND ORDER
ASYMPTOTIC COMPARISON OF THE ESTIMATORS FOR THE DOUBLE EXPONENTIAL
DISTRIBUTIONS 115 CHAPTER 6. HIGHER ORDER ASYMPTOTICS IN ESTIMATION FOR
TWO-SIDED WEIBULL TYPE DISTRIBUTIONS 124 6.1. THE 2A-TH ORDER ASYMPTOTIC
BOUND FOR THE DISTRIBUTION OF 2A-TH ORDER AMU ESTIMATORS 124 6.2. PROOFS
OF LEMMAS AND THEOREM IN SECTION 6.1 127 6.3. THE 2A-TH ORDER ASYMPTOTIC
DISTRIBUTION OF THE MAXIMUM LIKELIHOOD ESTIMATOR 135 6.4. THE AMOUNT OF
THE LOSS OF ASYMPTOTIC INFORMATION OF THE MAXIMUM LIKELIHOOD ESTIMATOR
145 CHAPTER 7. 3/2-TH AND SECOND ORDER ASYMPTOTICS OF THE GENERALIZED
BAYES ESTIMATORS FOR A FAMILY OF TRUNCATED DISTRIBUTIONS 147 7.1.
DEFINITIONS AND ASSUMPTIONS 147 7.2. GENERALIZED BAYES ESTIMATORS FOR A
FAMILY OF TRUNCATED DISTRIBUTIONS 149 7.3. SECOND ORDER ASYMPTOTIC BOUND
IN SYMMETRICALLY TRUNCATED DENSITIES 155 7.4. MAXIMUM PROBABILITY
ESTIMATION 158 7.5. EXAMPLES 164 7.6. SOME REMARKS 165 SUPPLEMENT. THE
BOUND FOR THE ASYMPTOTIC DISTRIBUTION OF ESTIMATORS WHEN THE MAXIMUM
ORDER OF CONSISTENCY DEPENDS ON THE PARAMETER 166 5.1. ORDER OF
CONSISTENCY DEPENDING ON THE PARAMETER . . . . 166 5.2. THE BOUND FOR
THE ASYMPTOTIC DISTRIBUTION OF AMU ESTIMATORS IN THE AUTOREGRESSIVE
PROCESS 169 REFERENCES 175 SUBJECT INDEX 182
|
| any_adam_object | 1 |
| author | Akahira, Masafumi 1945- Takeuchi, Kei 1933- |
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| dewey-full | 519.5/44 519.5/4420 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-search | 519.5/44 519.5/44 20 |
| dewey-sort | 3519.5 244 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| series2 | Lecture notes in statistics |
| spelling | Akahira, Masafumi 1945- Verfasser (DE-588)1089239793 aut Non-regular statistical estimation Masafumi Akahira ; Kei Takeuchi New York [u.a.] Springer 1995 VIII, 183 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in statistics 107 Estimation, Théorie de l' Estimation, théorie de l' ram Schattingstheorie gtt Statistiek gtt Statistique mathématique Statistique mathématique ram Statistik Mathematical statistics Estimation theory Schätztheorie (DE-588)4121608-8 gnd rswk-swf Schätztheorie (DE-588)4121608-8 s DE-604 Takeuchi, Kei 1933- Verfasser (DE-588)170069389 aut Lecture notes in statistics 107 (DE-604)BV002447846 107 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006955707&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Akahira, Masafumi 1945- Takeuchi, Kei 1933- Non-regular statistical estimation Lecture notes in statistics Estimation, Théorie de l' Estimation, théorie de l' ram Schattingstheorie gtt Statistiek gtt Statistique mathématique Statistique mathématique ram Statistik Mathematical statistics Estimation theory Schätztheorie (DE-588)4121608-8 gnd |
| subject_GND | (DE-588)4121608-8 |
| title | Non-regular statistical estimation |
| title_auth | Non-regular statistical estimation |
| title_exact_search | Non-regular statistical estimation |
| title_full | Non-regular statistical estimation Masafumi Akahira ; Kei Takeuchi |
| title_fullStr | Non-regular statistical estimation Masafumi Akahira ; Kei Takeuchi |
| title_full_unstemmed | Non-regular statistical estimation Masafumi Akahira ; Kei Takeuchi |
| title_short | Non-regular statistical estimation |
| title_sort | non regular statistical estimation |
| topic | Estimation, Théorie de l' Estimation, théorie de l' ram Schattingstheorie gtt Statistiek gtt Statistique mathématique Statistique mathématique ram Statistik Mathematical statistics Estimation theory Schätztheorie (DE-588)4121608-8 gnd |
| topic_facet | Estimation, Théorie de l' Estimation, théorie de l' Schattingstheorie Statistiek Statistique mathématique Statistik Mathematical statistics Estimation theory Schätztheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006955707&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002447846 |
| work_keys_str_mv | AT akahiramasafumi nonregularstatisticalestimation AT takeuchikei nonregularstatisticalestimation |