Stochastic limit theory: an introduction for econometricians
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2002
|
| Ausgabe: | reprinted |
| Schriftenreihe: | Advanced texts in econometrics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 539 S. graph. Darst. |
| ISBN: | 0198774028 0198774036 |
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| 245 | 1 | 0 | |a Stochastic limit theory |b an introduction for econometricians |c James Davidson |
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Datensatz im Suchindex
| _version_ | 1804138659289497600 |
|---|---|
| adam_text | Contents
Preface
xiii
Mathematical Symbols and Abbreviations
xix
Part I: Mathematics
1.
Sets and Numbers
1.1
Basic Set Theory
3
1.2
Countable Sets
8
1.3
The Real Continuum
10
1.4
Sequences of Sets
12
1.5
Classes of Subsets
13
1.6
Sigma Fields IS
2.
Limits and Continuity
2.1
The Topology of the Real Line
20
2.2
Sequences and Limits
23
2.3
Functions and Continuity
27
2.4
Vector Sequences and Functions
29
2.5
Sequences of Functions
30
2.6
Summability and Order Relations
31
2.7
Arrays
33
3.
Measure
3.1
Measure Spaces
36
3.2
The Extension Theorem
40
3.3
Non-measurability
46
3.4
Product Spaces
48
3.5
Measurable Transformations
50
3.6
Borei
Functions
55
4.
Integration
4.1
Construction of the Integral
57
4.2
Properties of the Integral
61
4.3
Product Measure and Multiple Integrals
64
4.4
The Radon-Nikodym Theorem
69
5.
Metric Spaces
5.1
Distances and Metrics
75
5.2
Separability and Completeness
78
5.3
Examples
82
vii
vii/
Contents
5.4
Mappings on Metric Spaces
84
5.5
Function Spaces
87
6.
Topology
6.1
Topologica!
Spaces
93
6.2
Countability and Compactness
94
6.3
Separation Properties
97
6.4
Weak Topologies
101
6.5
The Topology of Product Spaces
102
6.6
Embedding and Metrization
105
Part II: Probability
7.
Probability Spaces
7.1
Probability Measures 111
7.2
Conditional Probability
113
7.3
Independence
114
7.4
Product Spaces
115
8.
Random Variables
8.1
Measures on the Line
117
8.2
Distribution Functions
117
8.3
Examples
122
8.4
Multivariate Distributions
124
8.5
Independent Random Variables
126
9.
Expectations
9.1
Averages and Integrals
128
9.2
Expectations of Functions of X
130
9.3
Theorems for the Probabilist s Toolbox
132
9.4
Multivariate Distributions
135
9.5
More Theorems for the Toolbox
137
9.6
Random Variables Depending on a Parameter
140
10.
Conditioning
10.1
Conditioning in Product Measures
143
10.2
Conditioning on a Sigma Field
145
10.3
Conditional Expectations
147
10.4
Some Theorems on Conditional Expectations
149
10.5
Relationships between Subfields
154
10.6
Conditional Distributions
157
11.
Characteristic Functions
11.1
The Distribution of Sums of Random Variables
161
11.2
Complex Numbers
162
Contents ix
11.3
The Theory of Characteristic Functions
164
11.4
The Inversion Theorem
168
11.5
The Conditional Characteristic Function
171
Part III: Theory of Stochastic Processes
12.
Stochastic Processes
12.1
Basic Ideas and Terminology
177
12.2
Convergence of Stochastic Sequences
178
12.3
The Probability Model
179
12.4
The Consistency Theorem
183
12.5
Uniform and Limiting Properties
186
12.6
Uniform Integrability
188
13.
Dependence
13.1
Shift Transformations
191
13.2
Independence and Stationarity
192
13.3
Invariant Events
195
13.4
Ergodicity and Mixing
199
13.5
Subfields and Regularity
203
13.6
Strong and Uniform Mixing
206
14.
Mixing
14.1
Mixing Sequences of Random Variables
209
14.2
Mixing Inequalities
211
14.3
Mixing in Linear Processes
215
14.4
Sufficient Conditions for Strong and Uniform Mixing
219
15.
Martingales
15.1
Sequential Conditioning
229
15.2
Extensions of the Martingale Concept
232
15.3
Martingale Convergence
235
15.4
Convergence and the Conditional Variances
238
15.5
Martingale Inequalities
240
16.
Mixingales
16.1
Definition and Examples
247
16.2
Telescoping Sum Representations
249
16.3
Maximal Inequalities
252
16.4
Uniform Square-integrability
257
17.
Near-Epoch Dependence
17.1
Definition and Examples
261
17.2
Near-Epoch Dependence and Mixingales
264
Contents
17.3
Near-Epoch Dependence and Transformations
267
17.4
Approximability
273
Part IV: The Law of Large Numbers
18.
Stochastic Convergence
18.1
Almost Sure Convergence
281
18.2
Convergence in Probability
284
18.3
Transformations and Convergence
285
18.4
Convergence in Lp Norm
287
18.5
Examples
288
18.6
Laws of Large Numbers
289
19.
Convergence in Lp-Norm
19.1
Weak Laws by Mean-Square Convergence
293
19.2
Almost Sure Convergence by the Method of Subsequences
295
19.3
A Martingale Weak Law
298
19.4
A Mixingale Weak Law
302
19.5
Approximable Processes
304
20.
The Strong Law of Large Numbers
20.1
Technical Tricks for Proving LLNs
306
20.2
The Case of Independence
311
20.3
Martingale Strong Laws
313
20.4
Conditional Variances and Random Weighting
316
20.5
Two Strong Laws for Mixingales
318
20.6
Near-epoch Dependent and Mixing Processes
323
21.
Uniform Stochastic Convergence
21.1
Stochastic Functions on a Parameter Space
327
21.2
Pointwise and Uniform Stochastic Convergence
330
21.3
Stochastic Equicontinuity
335
21.4
Generic Uniform Convergence
337
21.5
Uniform Laws of Large Numbers
340
Part V: The Central Limit Theorem
22.
Weak Convergence of Distributions
22.1
Basic Concepts
347
22.2
The Skorokhod Representation Theorem
350
22.3
Weak Convergence and Transformations
355
22.4
Convergence of Moments and Characteristic Functions
357
22.5
Criteria for Weak Convergence
359
22.6
Convergence of Random Sums
361
Contents xi
23.
The Classical Central Limit Theorem
23.1
The i.i.d. Case
364
23.2
Independent Heterogeneous Sequences
368
23.3
Feller s Theorem and Asymptotic Negligibility
373
23.4
The Case of Trending Variances
377
24.
CLTs for Dependent Processes
24.1
A General Convergence Theorem
380
24.2
The Martingale Case
383
24.3
Stationary Ergodic Sequences
: 385
24.4
The CLT for NED Functions of Mixing Processes
386
24.5
Proving the CLT by the Bernstein Blocking Method
391
25.
Some Extensions
25.1
The CLT with Estimated Normalization
399
25.2
The CLT with Random Norming
403
25.3
The Multivariate CLT
405
25.4
Error Estimation
407
Part VI: The Functional Central Limit Theorem
26.
Weak Convergence in Metric Spaces
26.1
Probability Measures on a Metric Space
413
26.2
Measures and Expectations
416
26.3
Weak Convergence
418
26.4
Metrizing the Space of Measures
422
26.5
Tightness and Convergence
427
26.6
Skorokhod s Representation
431
27.
Weak Convergence in a Function Space
27.1
Measures on Function Spaces
434
27.2
The Space
С
437
27.3
Measures on
С
440
27.4
Brownian Motion
442
27.5
Weak Convergence on
С
447
27.6
The Functional Central Limit Theorem
449
27.7
The Multivariate Case
453
28.
Cadlag Functions
28.1
The Space
D
456
28.2
Metrizing
D
459
28.3
Billingsley s Metric
461
28.4
Measures on
D
465
xii Contents
28.5 Prokhorov s
Metric
467
28.6
Compactness and Tightness in
D
469
29.
FCLTs for Dependent Variables
29.1
The Distribution of Continuous Functions on
D
474
29.2
Asymptotic Independence
479
29.3
The FCLT for NED Functions of Mixing Processes
481
29.4
Transformed Brownian Motion
485
29.5
The Multivariate Case
490
30.
Weak Convergence to Stochastic Integrals
30.1
Weak Limit Results for Random Functionals
496
30.2
Stochastic Processes in Continuous Time
500
30.3
Stochastic Integrals
503
30.4
Convergence to Stochastic Integrals
509
Notes
517
References
519
Index
527
|
| any_adam_object | 1 |
| author | Davidson, James |
| author_facet | Davidson, James |
| author_role | aut |
| author_sort | Davidson, James |
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| building | Verbundindex |
| bvnumber | BV035342422 |
| callnumber-first | H - Social Science |
| callnumber-label | HB139 |
| callnumber-raw | HB139.D367 1994 |
| callnumber-search | HB139.D367 1994 |
| callnumber-sort | HB 3139 D367 41994 |
| callnumber-subject | HB - Economic Theory and Demography |
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| ctrlnum | (OCoLC)315818843 (DE-599)BVBBV035342422 |
| dewey-full | 330/.01/5120 519.2 330.015195 330/.01/51 |
| dewey-hundreds | 300 - Social sciences 500 - Natural sciences and mathematics |
| dewey-ones | 330 - Economics 519 - Probabilities and applied mathematics |
| dewey-raw | 330/.01/51 20 519.2 330.015195 330/.01/51 |
| dewey-search | 330/.01/51 20 519.2 330.015195 330/.01/51 |
| dewey-sort | 3330 11 251 220 |
| dewey-tens | 330 - Economics 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | reprinted |
| format | Book |
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| id | DE-604.BV035342422 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:31:42Z |
| institution | BVB |
| isbn | 0198774028 0198774036 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017146696 |
| oclc_num | 315818843 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 DE-703 DE-N2 DE-739 DE-523 |
| owner_facet | DE-355 DE-BY-UBR DE-11 DE-703 DE-N2 DE-739 DE-523 |
| physical | XXII, 539 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series2 | Advanced texts in econometrics |
| spelling | Davidson, James Verfasser aut Stochastic limit theory an introduction for econometricians James Davidson reprinted Oxford [u.a.] Oxford Univ. Press 2002 XXII, 539 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Advanced texts in econometrics Econometrics Limit theorems (Probability theory) Stochastic processes Ökonometrie (DE-588)4132280-0 gnd rswk-swf Zentraler Grenzwertsatz (DE-588)4067618-3 gnd rswk-swf Grenzwertsatz (DE-588)4158163-5 gnd rswk-swf Stochastisches Integral (DE-588)4126478-2 gnd rswk-swf Martingal (DE-588)4126466-6 gnd rswk-swf Stochastik (DE-588)4121729-9 gnd rswk-swf Stochastische Konvergenz (DE-588)4183376-4 gnd rswk-swf Martingal (DE-588)4126466-6 s Zentraler Grenzwertsatz (DE-588)4067618-3 s DE-604 Stochastisches Integral (DE-588)4126478-2 s Stochastische Konvergenz (DE-588)4183376-4 s Grenzwertsatz (DE-588)4158163-5 s Ökonometrie (DE-588)4132280-0 s Stochastik (DE-588)4121729-9 s 1\p DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017146696&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Davidson, James Stochastic limit theory an introduction for econometricians Econometrics Limit theorems (Probability theory) Stochastic processes Ökonometrie (DE-588)4132280-0 gnd Zentraler Grenzwertsatz (DE-588)4067618-3 gnd Grenzwertsatz (DE-588)4158163-5 gnd Stochastisches Integral (DE-588)4126478-2 gnd Martingal (DE-588)4126466-6 gnd Stochastik (DE-588)4121729-9 gnd Stochastische Konvergenz (DE-588)4183376-4 gnd |
| subject_GND | (DE-588)4132280-0 (DE-588)4067618-3 (DE-588)4158163-5 (DE-588)4126478-2 (DE-588)4126466-6 (DE-588)4121729-9 (DE-588)4183376-4 |
| title | Stochastic limit theory an introduction for econometricians |
| title_auth | Stochastic limit theory an introduction for econometricians |
| title_exact_search | Stochastic limit theory an introduction for econometricians |
| title_full | Stochastic limit theory an introduction for econometricians James Davidson |
| title_fullStr | Stochastic limit theory an introduction for econometricians James Davidson |
| title_full_unstemmed | Stochastic limit theory an introduction for econometricians James Davidson |
| title_short | Stochastic limit theory |
| title_sort | stochastic limit theory an introduction for econometricians |
| title_sub | an introduction for econometricians |
| topic | Econometrics Limit theorems (Probability theory) Stochastic processes Ökonometrie (DE-588)4132280-0 gnd Zentraler Grenzwertsatz (DE-588)4067618-3 gnd Grenzwertsatz (DE-588)4158163-5 gnd Stochastisches Integral (DE-588)4126478-2 gnd Martingal (DE-588)4126466-6 gnd Stochastik (DE-588)4121729-9 gnd Stochastische Konvergenz (DE-588)4183376-4 gnd |
| topic_facet | Econometrics Limit theorems (Probability theory) Stochastic processes Ökonometrie Zentraler Grenzwertsatz Grenzwertsatz Stochastisches Integral Martingal Stochastik Stochastische Konvergenz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017146696&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT davidsonjames stochasticlimittheoryanintroductionforeconometricians |