Higher order asymptotics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hayward, Calif.
Inst. of Math. Stat. [u.a.]
1994
|
| Series: | NSF-CBMS regional conference series in probability and statistics
4 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 111 S. |
| ISBN: | 0940600315 |
Staff View
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Record in the Search Index
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| adam_text | Titel: Higher order asymptotics
Autor: Gosh, Jayanta K.
Jahr: 1994
Contents
Preface vii
chapter 1: Introduction 1
1.1 Overview 1
1.2 First Order Efficiency 2
1.3 Third Order Efficiency 4
chapter 2: Edgeworth Expansions, Curved Exponentials and Fisher
Consistent Estimates 6
2.1 Edgeworth Expansions for Functions of Sample Mean 6
2.2 Remarks on the Proof 11
2.3 Remarks on Assumptions, Extensions, Background and Other
Applications 12
2.4 Curved Exponential Families and Fisher Consistent Estimates 13
2.5 Maximum Likelihood Estimator for Curved Exponentials 15
2.6 Maximum Likelihood Estimator in the General Regular Case 16
2.7 Remarks on Expansion of Asymptotic Mean, Variance and Risk 19
2.8 Problems 20
chapter 3: Third Order Efficiency for Curved Exponentials 22
3.1 The Main Result 22
3.2 Third Order Efficient Approximate Solution of Likelihood Equation 32
3.3 Example 2.3 (Berkson s Bioassay Example) Revisited 33
3.4 Multiparameter Extensions 34
3.5 Example 2.4 (Behrens-Fisher) Revisited 34
3.6 Hodges-Lehmann Deficiency 35
3.7 Asymptotic Sufficiency 36
3.8 Third Order Efficiency and Bhattacharya Bounds 37
chapter 4: Curvature and Information Loss 38
4.1 Curvature 38
4.2 Geometry of Information Loss 40
4.3 Curvature and Connection 42
4.4 Asymptotic Ancillaries and Conditional Loss of Information 43
vi HIGHER ORDER ASYMPTOTICS
chapter 5: Expansion of the Posterior, Bayes Estimate and Bayes Risk 45
5.1 Expansion of the Posterior 45
5.2 Expansion of the Bayes Estimate and Bayes Risk 49
chapter 6: Third Order Efficiency, Admissibility and Minimaxity 53
6.1 Third Order Efficiency in the General Case 53
6.2 Remarks on General Third Order Efficiency Results and Proofs 55
6.3 Median Unbiasedness and Matching Bias 55
6.4 First Order Efficiency Implies Second Order Efficiency 57
6.5 Strongest Third Order Efficiency Theorems for Fisher Consistent,
First Order Efficiency Estimates and Curved Exponentials 57
6.6 Uniformity to Third Order and Third Order Superefficiency 57
6.7 Third Order Admissibility 58
6.8 Berkson s Example Revisited 59
6.9 Third Order Minimaxity 60
6.10 Where Do We Go From Here? 64
chapter 7: Small Sample Efficiency 66
7.1 Introduction 66
7.2 A Lower Bound to Bayes Risk 67
7.3 A Lower Bound to the Local Minimax Risk 70
7.4 A Third Order Efficiency Proof that X is the Minimum Variance
Unbiased Estimate of the Normal Mean 72
7.5 Problems 72
chapter 8: Magic Formula, Bartlett Correction and Matching
Probabilities 74
8.1 Introduction 74
8.2 The Magic Formula 74
8.3 Bayesian and Frequentisi Bartlett Correction 76
8.4 Matching Probabilities and Confidence Sets 80
chapter 9: Noninformative Priors 86
9.1 Introduction 86
9.2 Reference Priors 87
9.3 Noninformative Priors via Matching Posterior and
Frequentisi Probabilities 90
9.4 Discussion of Assumptions and Interpretation 97
9.5 Comments on Reference and Probability Matching
Noninformative Priors 97
chapter 10: The New Likelihoods and the Neyman-Scott Problems 99
10.1 Introduction 99
10.2 Conditional and Adjusted Likelihood 99
10.3 Neyman-Scott Problems 101
Bibliography 106
|
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| id | DE-604.BV024974010 |
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| indexdate | 2024-07-09T22:24:51Z |
| institution | BVB |
| isbn | 0940600315 |
| language | English |
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| physical | VIII, 111 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Inst. of Math. Stat. [u.a.] |
| record_format | marc |
| series2 | NSF-CBMS regional conference series in probability and statistics |
| spelling | Ghosh, Jayanta K. Verfasser (DE-588)124691935 aut Higher order asymptotics Jayantha K. Ghosh Hayward, Calif. Inst. of Math. Stat. [u.a.] 1994 VIII, 111 S. txt rdacontent n rdamedia nc rdacarrier NSF-CBMS regional conference series in probability and statistics 4 National Science Foundation Conference Board of the Mathematical Sciences NSF-CBMS regional conference series in probability and statistics 4 (DE-604)BV008437408 4 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019641609&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ghosh, Jayanta K. Higher order asymptotics |
| title | Higher order asymptotics |
| title_auth | Higher order asymptotics |
| title_exact_search | Higher order asymptotics |
| title_full | Higher order asymptotics Jayantha K. Ghosh |
| title_fullStr | Higher order asymptotics Jayantha K. Ghosh |
| title_full_unstemmed | Higher order asymptotics Jayantha K. Ghosh |
| title_short | Higher order asymptotics |
| title_sort | higher order asymptotics |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019641609&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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