Weak convergence and empirical processes: with applications to statistics
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Springer
[1996]
|
| Series: | Springer series in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 467 - 486 |
| Physical Description: | XVI, 508 S. |
| ISBN: | 0387946403 9781475725476 |
Staff View
MARC
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| 100 | 1 | |a Vaart, Aad W. van der |d 1959- |0 (DE-588)114474680 |4 aut | |
| 245 | 1 | 0 | |a Weak convergence and empirical processes |b with applications to statistics |c Aad W. van der Vaart ; Jon A. Wellner |
| 264 | 1 | |a New York |b Springer |c [1996] | |
| 264 | 4 | |c © 1996 | |
| 300 | |a XVI, 508 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Springer series in statistics | |
| 500 | |a Literaturverz. S. 467 - 486 | ||
| 650 | 4 | |a Stochastic processes | |
| 650 | 4 | |a Convergence | |
| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 4 | |a Sampling (Statistics) | |
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Record in the Search Index
| _version_ | 1804125315934453760 |
|---|---|
| adam_text | AAD W. VAN DER VAART JO
N A
. WELLNER
WEAK CONVERGENCE
AND EMPIRICAL PROCESSES
WITH APPLICATIONS T
O STATISTICS
SPRINGER
CONTENTS
PREFAC
E VII
READIN
G GUID
E XI
1. STOCHASTI
C CONVERGENC
E 1
1.1. INTRODUCTIO
N 2
1.2. OUTE
R INTEGRAL
S AN
D MEASURABL
E MAJORANT
S 6
1.3. WEAK CONVERGENCE 16
1.4. PRODUC
T SPACES 29
1.5. SPACES OF BOUNDE
D FUNCTION
S 34
1.6. SPACES OF LOCALLY BOUNDE
D FUNCTION
S 43
1.7. TH
E BALL SIGMA-FIELD AN
D MEASURABILIT
Y OF SUPREM
A 45
1.8. HILBER
T SPACES 49
1.9. CONVERGENCE: ALMOS
T SURELY AN
D IN PROBABILIT
Y 52
1.10. CONVERGENCE: WEAK, ALMOST UNIFORM, AN
D IN PROBABILIT
Y ..
. 57
1.11. REFINEMENTS 67
1.12. UNIFORMITY AN
D METRIZATIO
N 71
NOTES
75
XI
V CONTENTS
2
. EMPIRICA
L PROCESSE
S 79
2.1
. INTRODUCTIO
N 80
2.1.1
. OVERVIEW OF CHAPTER
S 2.3-2.1
4 83
2.1.2. ASYMPTOTI
C EQUICONTINUIT
Y 89
2.1.3. MAXIMA
L INEQUALITIE
S 90
*2.1.4. TH
E CENTRA
L LIMIT THEORE
M IN BANAC
H SPACES ...
. 91
2.2. MAXIMA
L INEQUALITIE
S AN
D COVERING NUMBER
S 95
2.2.1
. SUB-GAUSSIA
N INEQUALITIE
S 100
2.2.2. BERNSTEIN
S INEQUALIT
Y 102
*2.2.3
. TIGHTNES
S UNDE
R A
N INCREMEN
T BOUN
D 104
2.3
. SYMMETRIZATIO
N AN
D MEASURABILIT
Y 107
2.3.1
. SYMMETRIZATIO
N 107
*2.3.2. MORE SYMMETRIZATIO
N IL
L
*2.3.3
. SEPARABL
E VERSIONS 115
2.4. GLIVENKO-CANTELLI THEOREM
S 122
2.5
. DONSKE
R THEOREM
S 127
2.5.1
. UNIFORM ENTROP
Y 127
2.5.2. BRACKETIN
G 129
2.6. UNIFORM ENTROP
Y NUMBER
S 134
2.6.1
. VC-CLASSES OF SET
S 134
2.6.2. VC-CLASSES OF FUNCTION
S 140
2.6.3
. CONVEX HULLS AN
D VC-HULL CLASSES 142
2.6.4. VC-MAJOR CLASSES 145
2.6.5
. EXAMPLE
S AN
D PERMANENC
E PROPERTIE
S 146
2.7. BRACKETIN
G NUMBER
S 154
2.7.1
. SMOOT
H FUNCTION
S AN
D SET
S 154
2.7.2. MONOTON
E FUNCTION
S 159
2.7.3. CLOSED CONVEX SETS AN
D CONVEX FUNCTION
S 162
2.7.4. CLASSES THA
T AR
E LIPSCHITZ IN A PARAMETE
R 164
2.8. UNIFORMIT
Y IN TH
E UNDERLYIN
G DISTRIBUTIO
N 166
2.8.1
. GLIVENKO-CANTELLI THEOREM
S 166
2.8.2. DONSKER THEOREM
S 168
2.8.3
. CENTRA
L LIMI
T THEORE
M UNDE
R SEQUENCES 173
2.9. MULTIPLIE
R CENTRA
L LIMIT THEOREM
S 176
2.10. PERMANENC
E OF TH
E DONSKER PROPERT
Y 190
2.10.1
. CLOSURES AN
D CONVEX HULLS 190
2.10.2. LIPSCHITZ TRANSFORMATION
S 192
2.10.3. PERMANENC
E OF TH
E UNIFORM ENTROP
Y BOUN
D 198
2.10.4. PARTITION
S OF TH
E SAMPL
E SPAC
E 200
2.11
. TH
E CENTRA
L LIMI
T THEORE
M FOR PROCESSE
S 205
2.11.1
. RANDO
M ENTROP
Y 205
2.11.2. BRACKETIN
G 210
2.11.3. CLASSES OF FUNCTION
S CHANGIN
G WIT
H N 220
2.12. PARTIAL-SU
M PROCESSE
S 225
CONTENTS XV
2.12.1. THE SEQUENTIAL EMPIRICAL PROCESS 225
2.12.2. PARTIAL-SUM PROCESSES ON LATTICES 228
2.13. OTHER DONSKER CLASSES 232
2.13.1. SEQUENCES 232
2.13.2. ELLIPTICAL CLASSES 233
2.13.3. CLASSES OF SETS 236
2.14. TAIL BOUNDS 238
2.14.1. FINITE ENTROPY INTEGRALS 238
2.14.2. UNIFORMLY BOUNDED CLASSES 245
2.14.3. DEVIATIONS FROM THE MEAN 254
2.14.4. PROOF OF THEOREM 2.14.13 257
NOTES
269
3. STATISTICAL APPLICATIONS 277
3.1. INTRODUCTION 278
3.2. M-ESTIMATORS 284
3.2.1. THE ARGMAX THEOREM 285
3.2.2. RATE OF CONVERGENCE 289
3.2.3. EXAMPLES 294
3.2.4. LINEARIZATION 300
3.3. Z-ESTIMATORS 309
3.4. RATES OF CONVERGENCE 321
3.4.1. MAXIMUM LIKELIHOOD 326
3.4.2. CONCAVE PARAMETRIZATIONS 330
3.4.3. LEAST SQUARES REGRESSION 331
3.4.4. LEAST-ABSOLUTE-DEVIATION REGRESSION 336
3.5. RANDOM SAMPLE SIZE, POISSONIZATION AND KAC PROCESSES . . . 339
3.5.1. RANDOM SAMPLE SIZE . 339
3.5.2. POISSONIZATION 341
3.6. THE BOOTSTRAP 345
3.6.1. THE EMPIRICAL BOOTSTRAP 345
3.6.2. THE EXCHANGEABLE BOOTSTRAP 353
3.7. THE TWO-SAMPLE PROBLEM 360
3.7.1. PERMUTATION EMPIRICAL PROCESSES 362
3.7.2. TWO-SAMPLE BOOTSTRAP 365
3.8. INDEPENDENCE EMPIRICAL PROCESSES 367
3.9. THE DELTA-METHOD 372
3.9.1. MAIN RESULT 372
3.9.2. GAUSSIAN LIMITS 376
3.9.3. THE DELTA-METHOD FOR THE BOOTSTRAP 377
3.9.4. EXAMPLES OF THE DELTA-METHOD 381
3.10. CONTIGUITY 401
3.10.1. THE EMPIRICAL PROCESS 406
XV
I CONTENTS
3.10.2. CHANGE-POINT ALTERNATIVES 408
3.11. CONVOLUTION AND MINIMAX THEOREMS 412
3.11.1. EFFICIENCY OF THE EMPIRICAL DISTRIBUTION 420
NOTES
423
A
. APPENDI
X 429
A.I
. INEQUALITIES 430
A.2. GAUSSIAN PROCESSES 437
A.2.1. INEQUALITIES AND GAUSSIAN COMPARISON 437
A.2.2. EXPONENTIAL BOUNDS 442
A.2.3. MAJORIZING MEASURES 445
A.2.4. FURTHER RESULTS 447
A.3. RADEMACHER PROCESSES 449
A.4. ISOPERIMETRIC INEQUALITIES FOR PRODUCT MEASURES 451
A.5. SOME LIMIT THEOREMS 456
A.6. MORE INEQUALITIES 459
A.6.1. BINOMIAL RANDOM VARIABLES 459
A.6.2. MULTINOMIAL RANDOM VECTORS 462
A.6.3. RADEMACHER SUMS 463
NOTES
465
REFERENCE
S 467
AUTHO
R INDE
X 487
SUBJEC
T INDE
X 493
LIS
T OF SYMBOL
S 506
|
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| author | Vaart, Aad W. van der 1959- Wellner, Jon A. |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV010829375 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:59:37Z |
| institution | BVB |
| isbn | 0387946403 9781475725476 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007237899 |
| oclc_num | 247036857 |
| open_access_boolean | |
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| physical | XVI, 508 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spelling | Vaart, Aad W. van der 1959- (DE-588)114474680 aut Weak convergence and empirical processes with applications to statistics Aad W. van der Vaart ; Jon A. Wellner New York Springer [1996] © 1996 XVI, 508 S. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Literaturverz. S. 467 - 486 Stochastic processes Convergence Distribution (Probability theory) Sampling (Statistics) Empirischer Prozess (DE-588)4224810-3 gnd rswk-swf Stochastische Konvergenz (DE-588)4183376-4 gnd rswk-swf Empirischer Prozess (DE-588)4224810-3 s Stochastische Konvergenz (DE-588)4183376-4 s DE-604 Wellner, Jon A. aut Erscheint auch als Onlineausgabe 978-1-4757-2545-2 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007237899&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vaart, Aad W. van der 1959- Wellner, Jon A. Weak convergence and empirical processes with applications to statistics Stochastic processes Convergence Distribution (Probability theory) Sampling (Statistics) Empirischer Prozess (DE-588)4224810-3 gnd Stochastische Konvergenz (DE-588)4183376-4 gnd |
| subject_GND | (DE-588)4224810-3 (DE-588)4183376-4 |
| title | Weak convergence and empirical processes with applications to statistics |
| title_auth | Weak convergence and empirical processes with applications to statistics |
| title_exact_search | Weak convergence and empirical processes with applications to statistics |
| title_full | Weak convergence and empirical processes with applications to statistics Aad W. van der Vaart ; Jon A. Wellner |
| title_fullStr | Weak convergence and empirical processes with applications to statistics Aad W. van der Vaart ; Jon A. Wellner |
| title_full_unstemmed | Weak convergence and empirical processes with applications to statistics Aad W. van der Vaart ; Jon A. Wellner |
| title_short | Weak convergence and empirical processes |
| title_sort | weak convergence and empirical processes with applications to statistics |
| title_sub | with applications to statistics |
| topic | Stochastic processes Convergence Distribution (Probability theory) Sampling (Statistics) Empirischer Prozess (DE-588)4224810-3 gnd Stochastische Konvergenz (DE-588)4183376-4 gnd |
| topic_facet | Stochastic processes Convergence Distribution (Probability theory) Sampling (Statistics) Empirischer Prozess Stochastische Konvergenz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007237899&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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