Elements of modern asymptotic theory with statistical applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Manchester u.a.
Manchester Univ. Press
1993
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 264 S. graph. Darst. |
| ISBN: | 0719030528 0719030536 |
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MARC
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| 245 | 1 | 0 | |a Elements of modern asymptotic theory with statistical applications |c Brendan McCabe and Andrew Tremayne |
| 264 | 1 | |a Manchester u.a. |b Manchester Univ. Press |c 1993 | |
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Record in the Search Index
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| adam_text | Contents
Preface ix
1 Probability and measure 1
1.1 Introduction 1
1.2 Finite sample spaces and probability measure 2
1.3 Countably infinite sample spaces and probability measure 7
1.4 Uncountably infinite sample spaces and probability 10
measure
1.5 Multi dimensional sample spaces 17
1.6 Summary 17
2 Random variables and distributions in statistics 19
2.1 Introduction 19
2.2 Distribution functions 20
2.3 Random variables 23
2.4 The distribution or law of a random variable 25
2.5 Some basic theory of integration 26
2.6 Probability mass and density functions 33
2.7 Moments of random variables 36
2.8 Multivariate random variables 40
2.9 Independence 44
2.10 Summary 46
3 Concepts of asymptotic convergence 48
3.1 Introduction 48
vi Contents
3.2 Convergence in distribution 49
3.3 The Central Limit Theorem 54
3.4 Convergence in probability 63
3.5 Weak Law of Large Numbers 67
3.6 Convergence in rth mean 70
3.7 Almost sure convergence 73
3.8 Summary 80
4 Further asymptotic theory with applications in regression 82
4.1 Introduction 82
4.2 Consistency and asymptotic normality of least squares 84
4.3 Multivariate convergence 86
4.4 The Continuous Mapping Theorem 89
4.5 Consistency and asymptotic normality revisited 95
4.6 Some extensions 98
4.7 Estimating the disturbance variance 102
4.8 Instrumental variable estimation 103
4.9 Summary 105
5 Likelihood and associated concepts 106
5.1 Introduction 106
5.2 Some preliminary ideas 107
5.3 The likelihood function 108
5.4 Maximum likelihood estimation 110
5.5 The score function 114
5.6 Maximum likelihood via the score function 119
5.7 Information 123
5.8 The Cramer Rao inequality 126
5.9 Summary 128
6 Maximum likelihood and asymptotic theory 129
6.1 Introduction 129
6.2 Consistency and asymptotic efficiency 130
6.3 Asymptotic properties of maximum likelihood 131
6.4 The vector parameter case 136
6.5 Multiple roots 137
6.6 Some non regular cases 138
Contents vii
6.7 Non identically distributed random variables 140
6.8 Hypothesis testing 141
6.9 Nuisance parameters 149
6.10 Local Asymptotic Normality and power considerations 151
6.11 Summary 153
7 Metric spaces and stochastic processes 155
7.1 Introduction 155
7.2 Partial sum processes 156
7.3 Metric spaces 158
7.4 Stochastic processes 164
7.5 Summary 169
8 Brownian motion and weak convergence 171
8.1 Introduction 171
8.2 Brownian motion and the Brownian bridge 172
8.3 Convergence of stochastic processes 176
8.4 Skorohod constructions and embeddings 180
8.5 Donsker s Theorem 185
8.6 A multivariate version of Donsker s Theorem 187
8.7 A direct method for proving weak convergence 189
8.8 Summary 191
9 Applications of weak convergence 193
9.1 Introduction 193
9.2 Tests for structural change 193
9.3 Goodness of fit tests 196
9.4 Stochastic integration 198
9.5 Testing models for coefficient constancy 203
9.6 Integrated regressors 207
9.7 Testing for random walks 210
9.8 Summary 213
10 Dependent random variables and mixing 215
10.1 Introduction 215
10.2 Autoregressive and moving average models 216
10.3 Stationarity 220
10.4 Mixing processes 222
viii Contents
10.5 WLLN for stationary mixing sequences 225
10.6 The CLT and stationary mixing sequences 228
10.7 Why the CLT holds under mixing 230
10.8 Non stationary sequences and the FCLT 233
10.9 Summary 237
11 Dependent sequences and martingales 238
11.1 Introduction 238
11.2 Conditional probabilities and expectations 239
11.3 Elementary properties of martingales 243
11.4 Examples of martingales 245
11.5 Martingale convergence 251
11.6 Summary 253
References 255
Index 257
|
| any_adam_object | 1 |
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| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:12:15Z |
| institution | BVB |
| isbn | 0719030528 0719030536 |
| language | English |
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| physical | XI, 264 S. graph. Darst. |
| publishDate | 1993 |
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| publisher | Manchester Univ. Press |
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| spelling | MacCabe, Brendan Verfasser aut Elements of modern asymptotic theory with statistical applications Brendan McCabe and Andrew Tremayne Manchester u.a. Manchester Univ. Press 1993 XI, 264 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Asymptotische analyse gtt Hypothesetoetsing gtt Schattingstheorie gtt Statistische methoden gtt Estimation theory Asymptotic theory Statistical hypothesis testing Asymptotic theory Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Schätztheorie (DE-588)4121608-8 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Ökonometrie (DE-588)4132280-0 gnd rswk-swf Schätztheorie (DE-588)4121608-8 s Asymptotische Methode (DE-588)4287476-2 s DE-604 Statistik (DE-588)4056995-0 s Ökonometrie (DE-588)4132280-0 s Asymptotik (DE-588)4126634-1 s DE-188 Tremayne, Andrew Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005240133&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | MacCabe, Brendan Tremayne, Andrew Elements of modern asymptotic theory with statistical applications Asymptotische analyse gtt Hypothesetoetsing gtt Schattingstheorie gtt Statistische methoden gtt Estimation theory Asymptotic theory Statistical hypothesis testing Asymptotic theory Asymptotische Methode (DE-588)4287476-2 gnd Schätztheorie (DE-588)4121608-8 gnd Asymptotik (DE-588)4126634-1 gnd Statistik (DE-588)4056995-0 gnd Ökonometrie (DE-588)4132280-0 gnd |
| subject_GND | (DE-588)4287476-2 (DE-588)4121608-8 (DE-588)4126634-1 (DE-588)4056995-0 (DE-588)4132280-0 |
| title | Elements of modern asymptotic theory with statistical applications |
| title_auth | Elements of modern asymptotic theory with statistical applications |
| title_exact_search | Elements of modern asymptotic theory with statistical applications |
| title_full | Elements of modern asymptotic theory with statistical applications Brendan McCabe and Andrew Tremayne |
| title_fullStr | Elements of modern asymptotic theory with statistical applications Brendan McCabe and Andrew Tremayne |
| title_full_unstemmed | Elements of modern asymptotic theory with statistical applications Brendan McCabe and Andrew Tremayne |
| title_short | Elements of modern asymptotic theory with statistical applications |
| title_sort | elements of modern asymptotic theory with statistical applications |
| topic | Asymptotische analyse gtt Hypothesetoetsing gtt Schattingstheorie gtt Statistische methoden gtt Estimation theory Asymptotic theory Statistical hypothesis testing Asymptotic theory Asymptotische Methode (DE-588)4287476-2 gnd Schätztheorie (DE-588)4121608-8 gnd Asymptotik (DE-588)4126634-1 gnd Statistik (DE-588)4056995-0 gnd Ökonometrie (DE-588)4132280-0 gnd |
| topic_facet | Asymptotische analyse Hypothesetoetsing Schattingstheorie Statistische methoden Estimation theory Asymptotic theory Statistical hypothesis testing Asymptotic theory Asymptotische Methode Schätztheorie Asymptotik Statistik Ökonometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005240133&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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