Quasi-likelihood and its application: a general approach to optimal parameter estimation
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1997
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| Schriftenreihe: | Springer series in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 235 S. |
| ISBN: | 0387982256 |
Internformat
MARC
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| 100 | 1 | |a Heyde, Christopher C. |d 1939-2008 |e Verfasser |0 (DE-588)123400309 |4 aut | |
| 245 | 1 | 0 | |a Quasi-likelihood and its application |b a general approach to optimal parameter estimation |c Christopher C. Heyde |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1997 | |
| 300 | |a IX, 235 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer series in statistics | |
| 650 | 7 | |a Optimaliseren |2 gtt | |
| 650 | 7 | |a Parameters |2 gtt | |
| 650 | 7 | |a Schattingen |2 gtt | |
| 650 | 4 | |a Parameter estimation | |
| 650 | 0 | 7 | |a Parameterschätzung |0 (DE-588)4044614-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
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| 689 | 1 | 0 | |a Parameterschätzung |0 (DE-588)4044614-1 |D s |
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Datensatz im Suchindex
| _version_ | 1804126057540878336 |
|---|---|
| adam_text | Contents
Preface v
1 Introduction 1
1.1 The Brief 1
1.2 Preliminaries 1
1.3 The Gauss Markov Theorem 3
1.4 Relationship with the Score Function 6
1.5 The Road Ahead 7
1.6 The Message of the Book 10
1.7 Exercise 10
2 The General Framework 11
2.1 Introduction 11
2.2 Fixed Sample Criteria 11
2.3 Scalar Equivalences and Associated Results 19
2.4 Wedderbum s Quasi Likelihood 21
2.4.1 The Framework 21
2.4.2 Limitations 23
2.4.3 Generalized Estimating Equations 25
2.5 Asymptotic Criteria 26
2.6 A Semimartingale Model for Applications 30
2.7 Some Problem Cases for the Methodology 35
2.8 Complements and Exercises 38
3 An Alternative Approach: E Sufflciency 43
3.1 Introduction 43
3.2 Definitions and Notation 43
3.3 Results 46
3.4 Complement and Exercise 51
4 Asymptotic Confidence Zones of Minimum Size 53
4.1 Introduction 53
4.2 The Formulation 54
4.3 Confidence Zones: Theory 56
vii
viii CONTENTS
4.4 Confidence Zones: Practice 60
4.5 On Best Asymptotic Confidence Intervals 62
4.5.1 Introduction and Results 62
4.5.2 Proof of Theorem 4.1 64
4.6 Exercises 67
5 Asymptotic Quasi Likelihood 69
5.1 Introduction 69
5.2 The Formulation 71
5.3 Examples 79
5.3.1 Generalized Linear Model 79
5.3.2 Heteroscedastic Autoregressive Model 79
5.3.3 Whittle Estimation Procedure 82
5.3.4 Addendum to the Example of Section 5.1 87
5.4 Bibliographic Notes 88
5.5 Exercises 88
6 Combining Estimating Functions 91
6.1 Introduction 91
6.2 Composite Quasi Likelihoods 92
6.3 Combining Martingale Estimating Functions 93
6.3.1 An Example 98
6.4 Application. Nested Strata of Variation 99
6.5 State Estimation in Time Series 103
6.6 Exercises 104
7 Projected Quasi Likelihood 107
7.1 Introduction 107
7.2 Constrained Parameter Estimation 107
7.2.1 Main Results 109
7.2.2 Examples Ill
7.2.3 Discussion 112
7.3 Nuisance Parameters 113
7.4 Generalizing the E M Algorithm: The P S Method 116
7.4.1 From Log Likelihood to Score Function 117
7.4.2 From Score to Quasi Score 118
7.4.3 Key Applications 121
7.4.4 Examples 122
7.5 Exercises 127
8 Bypassing the Likelihood 129
8.1 Introduction 129
8.2 The REML Estimating Equations 129
8.3 Parameters in Diffusion Type Processes 131
8.4 Estimation in Hidden Markov Random Fields 136
8.5 Exercise 139
CONTENTS ix
9 Hypothesis Testing 141
9.1 Introduction 141
9.2 The Details 142
9.3 Exercise 145
10 Infinite Dimensional Problems 147
10.1 Introduction 147
10.2 Sieves 147
10.3 Semimartingale Models 148
11 Miscellaneous Applications 153
11.1 Estimating the Mean of a Stationary Process 153
11.2 Estimation for a Heteroscedastic Regression 159
11.3 Estimating the Infection Rate in an Epidemic 162
11.4 Estimating Population Size 164
11.5 Robust Estimation 169
11.5.1 Optimal Robust Estimating Functions 170
11.5.2 Example 173
11.6 Recursive Estimation 176
12 Consistency and Asymptotic Normality
for Estimating Functions 179
12.1 Introduction 179
12.2 Consistency 180
12.3 The SLLN for Martingales 186
12.4 The CLT for Martingales 190
12.5 Exercises 195
13 Complements and Strategies for Application 199
13.1 Some Useful Families of Estimating Functions 199
13.1.1 Introduction 199
13.1.2 Transform Martingale Families 199
13.1.3 Use of the Infinitesimal Generator of a Markov Process 200
13.2 Solution of Estimating Equations 201
13.3 Multiple Roots 202
13.3.1 Introduction 202
13.3.2 Examples 204
13.3.3 Theory 208
13.4 Resampling Methods 210
References 211
Index 227
|
| any_adam_object | 1 |
| author | Heyde, Christopher C. 1939-2008 |
| author_GND | (DE-588)123400309 |
| author_facet | Heyde, Christopher C. 1939-2008 |
| author_role | aut |
| author_sort | Heyde, Christopher C. 1939-2008 |
| author_variant | c c h cc cch |
| building | Verbundindex |
| bvnumber | BV011535686 |
| callnumber-first | Q - Science |
| callnumber-label | QA276 |
| callnumber-raw | QA276.8.H475 1997 |
| callnumber-search | QA276.8.H475 1997 |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 625f |
| ctrlnum | (OCoLC)36509963 (DE-599)BVBBV011535686 |
| dewey-full | 519.5/4421 519.5/44 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/44 21 519.5/44 |
| dewey-search | 519.5/44 21 519.5/44 |
| dewey-sort | 3519.5 244 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV011535686 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:11:24Z |
| institution | BVB |
| isbn | 0387982256 |
| language | English |
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| physical | IX, 235 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
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| series2 | Springer series in statistics |
| spelling | Heyde, Christopher C. 1939-2008 Verfasser (DE-588)123400309 aut Quasi-likelihood and its application a general approach to optimal parameter estimation Christopher C. Heyde New York [u.a.] Springer 1997 IX, 235 S. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Optimaliseren gtt Parameters gtt Schattingen gtt Parameter estimation Parameterschätzung (DE-588)4044614-1 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Parameterschätzung (DE-588)4044614-1 s DE-604 Stochastischer Prozess (DE-588)4057630-9 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007764360&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Heyde, Christopher C. 1939-2008 Quasi-likelihood and its application a general approach to optimal parameter estimation Optimaliseren gtt Parameters gtt Schattingen gtt Parameter estimation Parameterschätzung (DE-588)4044614-1 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4044614-1 (DE-588)4057630-9 |
| title | Quasi-likelihood and its application a general approach to optimal parameter estimation |
| title_auth | Quasi-likelihood and its application a general approach to optimal parameter estimation |
| title_exact_search | Quasi-likelihood and its application a general approach to optimal parameter estimation |
| title_full | Quasi-likelihood and its application a general approach to optimal parameter estimation Christopher C. Heyde |
| title_fullStr | Quasi-likelihood and its application a general approach to optimal parameter estimation Christopher C. Heyde |
| title_full_unstemmed | Quasi-likelihood and its application a general approach to optimal parameter estimation Christopher C. Heyde |
| title_short | Quasi-likelihood and its application |
| title_sort | quasi likelihood and its application a general approach to optimal parameter estimation |
| title_sub | a general approach to optimal parameter estimation |
| topic | Optimaliseren gtt Parameters gtt Schattingen gtt Parameter estimation Parameterschätzung (DE-588)4044614-1 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Optimaliseren Parameters Schattingen Parameter estimation Parameterschätzung Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007764360&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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