Asymptotic statistics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2000
|
| Edition: | 1. paperback ed. |
| Series: | Cambridge series in statistical and probabilistic mathematics
[3] |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XV, 443 S. graph. Darst. |
| ISBN: | 0521784506 0521496039 9780521784504 9780521496032 |
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MARC
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| 100 | 1 | |a Vaart, Aad W. van der |d 1959- |e Verfasser |0 (DE-588)114474680 |4 aut | |
| 245 | 1 | 0 | |a Asymptotic statistics |c A. W. van der Vaart |
| 250 | |a 1. paperback ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2000 | |
| 300 | |a XV, 443 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge series in statistical and probabilistic mathematics |v [3] | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Mathematical statistics |x Asymptotic theory | |
| 650 | 0 | 7 | |a Asymptotische Statistik |0 (DE-588)4203167-9 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804138448168157184 |
|---|---|
| adam_text | Contents
Preface
page
xiii
Notation
page
xv
1.
Introduction
1
1.1.
Approximate Statistical Procedures
1
1.2.
Asymptotic Optimality Theory
2
1.3.
Limitations
3
1.4.
The Index
я
4
2.
Stochastic Convergence
5
2.1.
Basic Theory
5
2.2.
Stochastic
о
and
О
Symbols
12
*2.3. Characteristic Functions
13
*2.4. Almost-Sure Representations
17
*2.5. Convergence of Moments
17
*2.6. Convergence-Determining Classes
18
*2.7. Law of the Iterated Logarithm
19
*2.8. Lindeberg-Feller Theorem
20
*2.9. Convergence in Total Variation
22
Problems
24
3.
Delta Method
25
3.1.
Basic Result
25
3.2.
Variance-Stabilizing Transformations
30
*3.3. Higher-Order Expansions
31
*3.4. Uniform Delta Method
32
*3.5. Moments
33
Problems
34
4.
Moment Estimators
35
4.1.
Method of Moments
35
*4.2. Exponential Families
37
Problems
40
5.
M- and Z-Estimators
41
S.I. Introduction
41
5.2.
Consistency
44
5.3.
AsvmDtotic Normality
51
VII
Contents
*5.4. Estimated Parameters
60
5.5.
Maximum Likelihood Estimators
61
*5.6. Classical Conditions
67
♦5.7.
One-Step Estimators
71
♦5.8.
Rates of Convergence
75
*5.9. Argmax Theorem
79
Problems
83
6.
Contiguity
85
6.1.
Likelihood Ratios
85
6.2.
Contiguity
87
Problems
91
7.
Local Asymptotic Normality
92
7.1.
Introduction
92
7.2.
Expanding the Likelihood
93
7.3.
Convergence to a Normal Experiment
97
7.4.
Maximum Likelihood
100
*7.5. Limit Distributions under Alternatives
103
♦7.6.
Local Asymptotic Normality
103
Problems
106
8.
Efficiency of Estimators
108
8.1.
Asymptotic Concentration
108
8.2.
Relative Efficiency
110
8.3.
Lower Bound for Experiments
111
8.4.
Estimating Normal Means
112
8.5.
Convolution Theorem
115
8.6.
Almost-Everywhere Convolution
Theorem
115
*8.7. Local Asymptotic Minimax Theorem
11?
*8.8. Shrinkage Estimators
119
*8.9. Achieving the Bound
120
•8.10.
Large Deviations
122
Problems
123
9.
Limits of Experiments
125
9.1.
Introduction
125
9.2.
Asymptotic Representation Theorem
126
9.3.
Asymptotic Normality
127
9.4.
Uniform Distribution
129
9.5
Pareto Distribution
130
9.6.
Asymptotic Mixed Normality
131
9 7.
Heuristics
136
Problems
137
10.
Bayes
Procedures
138
10.1.
Introduction
138
10.2.
Bemstem-von Mises
Theorem 14°
Contents
10.3. Point
Estimators
146
*10.4.
Consistency
149
Problems 152
11.
Projections
153
11.1.
Projections
153
11.2.
Conditional Expectation
155
11.3.
Projection onto Sums
157
*11.4. Hoeffding Decomposition
157
Problems
160
12.
tZ-Statistics
161
12.1.
One-Sample rZ-Statistics
161
12.2.
Two-Sample
řZ-statistics
165
♦12.3.
Degenerate
ÍZ-Statistics
167
Problems
171
13.
Rank, Sign, and Permutation Statistics
173
13.1.
Rank Statistics
173
13.2.
Signed Rank Statistics
181
13.3.
Rank Statistics for Independence
184
*13.4. Rank Statistics under Alternatives
184
13.5.
Permutation Tests
188
*13.6. Rank Central Limit Theorem
190
Problems
190
14.
Relative Efficiency of Tests
192
14.1.
Asymptotic Power Functions
192
14.2.
Consistency
199
14.3.
Asymptotic Relative Efficiency
201
*14.4. Other Relative Efficiencies
202
♦14.5. Rescaling
Rates
211
Problems
213
15.
Efficiency of Tests
215
15.1.
Asymptotic Representation Theorem
215
15.2.
Testing Normal Means
216
15.3.
Local Asymptotic Normality
218
15.4.
One-Sample Location
220
15.5.
Two-Sample Problems
223
Problems
226
16.
Likelihood Ratio Tests
227
16.1.
Introduction
227
♦16.2.
Taylor Expansion
229
16.3.
Using Local Asymptotic Normality
231
16.4.
Asymptotic Power Functions
236
Contents
16.5. Bartlett
Correction
238
Чб.б.
Bahadur Efficiency
238
Problems
241
17.
Chi-Square Tests
242
17.1.
Quadratic Forms in Normal Vectors
242
17.2.
Pearson Statistic
242
17.3.
Estimated Parameters
244
17.4.
Testing Independence
247
♦17.5.
Goodness-of-Fit Tests
248
*17.6. Asymptotic Efficiency
251
Problems
253
18.
Stochastic Convergence in Metric Spaces
255
18.1.
Metric and Normed Spaces
255
18.2.
Basic Properties
258
18.3.
Bounded Stochastic Processes
260
Problems
263
19.
Empirical Processes
265
19.1.
Empirical Distribution Functions
265
19.2.
Empirical Distributions
269
19.3.
Goodness-of-Fit Statistics
277
19.4.
Random Functions
279
19.5.
Changing Classes
282
19.6.
Maximal Inequalities
284
Problems
289
20.
Functional Delta Method
291
20.1. von
Mises
Calculus
291
20.2. Hadamard-Differentiable
Functions
2%
20.3.
Some Examples
298
Problems
303
304
304
305
310
312
315
316
316
318
320
323
324
23.
Bootstrap
326
21.
Quantiles and Order Statistics
21.1.
Weak Consistency
21.2.
Asymptotic Normality
21.3.
Median Absolute Deviation
21.4.
Extreme Values
Problems
22.
¿-Statistics
22.1.
Introduction
22.2.
Hájek
Projection
22.3.
Delta Method
22.4.
¿-Estimators for Location
Problems
Contents
23.1.
Introduction
23.2.
Consistency
23.3.
Higher-Order Correctness
Problems
24. Nonparametric
Density Estimation
24.1
Introduction
24.2
Kernel Estimators
24.3
Rate Optimality
24.4
Estimating a Unimodal Density
Problems
25. Semiparametric Models
25.1
Introduction
25.2
Banach and Hubert Spaces
25.3
Tangent Spaces and Information
25.4
Efficient Score Functions
25.5
Score and Information Operators
25.6
Testing
*25.7
Efficiency and the Delta Method
25.8
Efficient Score Equations
25.9
General Estimating Equations
25.10
Maximum Likelihood Estimators
25.11
Approximately Least-Favorable
Submodels
25.12
Likelihood Equations
Problems
References
Index
326
329
334
339
341
341
341
346
349
356
358
358
360
362
368
371
384
386
391
400
402
408
419
431
433
439
This book is an introduction to the field of asymptotic statistics. The treatment is both prac¬
tical and mathematically rigorous. In addition to most of the standard topics of an asymp-
totics course, including likelihood inference. M-estimation. the theory of asymptotic effi¬
ciency, ¿/-statistics, and rank procedures, the book presents recent research topics such
as semiparametric models, the bootstrap, and empirical processes and their applications.
The topics are organized from the central idea of approximation by limit experiments, which
gives the book one of its unifying themes. This entails mainly the local approximation of
the classical i.i.d. setup with smooth parameters by location experiments involving a sin¬
gle, normally distributed observation. Thus, even the standard subjects of asymptotic sta¬
tistics are presented in a novel way.
Suitable as a text for a graduate or Master s level statistics course, this book will also give
researchers in statistics, probability, and their applications an overview of the latest
research in asymptotic statistics.
|
| any_adam_object | 1 |
| author | Vaart, Aad W. van der 1959- |
| author_GND | (DE-588)114474680 |
| author_facet | Vaart, Aad W. van der 1959- |
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| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. paperback ed. |
| format | Book |
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| id | DE-604.BV035197219 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:28:21Z |
| institution | BVB |
| isbn | 0521784506 0521496039 9780521784504 9780521496032 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017003721 |
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| physical | XV, 443 S. graph. Darst. |
| publishDate | 2000 |
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| publisher | Cambridge Univ. Press |
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| series | Cambridge series in statistical and probabilistic mathematics |
| series2 | Cambridge series in statistical and probabilistic mathematics |
| spelling | Vaart, Aad W. van der 1959- Verfasser (DE-588)114474680 aut Asymptotic statistics A. W. van der Vaart 1. paperback ed. Cambridge [u.a.] Cambridge Univ. Press 2000 XV, 443 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge series in statistical and probabilistic mathematics [3] Hier auch später erschienene, unveränderte Nachdrucke Mathematical statistics Asymptotic theory Asymptotische Statistik (DE-588)4203167-9 gnd rswk-swf Asymptotische Statistik (DE-588)4203167-9 s DE-604 Cambridge series in statistical and probabilistic mathematics [3] (DE-604)BV011442366 3 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017003721&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017003721&sequence=000007&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Vaart, Aad W. van der 1959- Asymptotic statistics Cambridge series in statistical and probabilistic mathematics Mathematical statistics Asymptotic theory Asymptotische Statistik (DE-588)4203167-9 gnd |
| subject_GND | (DE-588)4203167-9 |
| title | Asymptotic statistics |
| title_auth | Asymptotic statistics |
| title_exact_search | Asymptotic statistics |
| title_full | Asymptotic statistics A. W. van der Vaart |
| title_fullStr | Asymptotic statistics A. W. van der Vaart |
| title_full_unstemmed | Asymptotic statistics A. W. van der Vaart |
| title_short | Asymptotic statistics |
| title_sort | asymptotic statistics |
| topic | Mathematical statistics Asymptotic theory Asymptotische Statistik (DE-588)4203167-9 gnd |
| topic_facet | Mathematical statistics Asymptotic theory Asymptotische Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017003721&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017003721&sequence=000007&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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