Probability for statisticians:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2000
|
| Schriftenreihe: | Springer texts in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Buchcover |
| Beschreibung: | XVII, 585 S. graph. Darst. |
| ISBN: | 0387989536 |
Internformat
MARC
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| 100 | 1 | |a Shorack, Galen R. |d 1939- |e Verfasser |0 (DE-588)122259122 |4 aut | |
| 245 | 1 | 0 | |a Probability for statisticians |c Galen R. Shorack |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2000 | |
| 300 | |a XVII, 585 S. |b graph. Darst. | ||
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| 490 | 0 | |a Springer texts in statistics | |
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| 650 | 7 | |a Waarschijnlijkheid (statistiek) |2 gtt | |
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| 650 | 0 | 7 | |a Wahrscheinlichkeit |0 (DE-588)4137007-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804128003525967872 |
|---|---|
| adam_text | Contents
Preface vii
Use of This Text xiii
Definition of Symbols xviii
Chapter 1. Measures
1. Basic Properties of Measures 1
2. Construction and Extension of Measures 12
3. Lebesgue Stieltjes Measures 18
Chapter 2. Measurable Functions and Convergence
1. Mappings and cr Fields 21
2. Measurable Functions 24
3. Convergence 29
4. Probability, RVs, and Convergence in Law 33
5. Discussion of Sub a Fields 35
Chapter 3. Integration
1. The Lebesgue Integral 37
2. Fundamental Properties of Integrals 40
3. Evaluating and Differentiating Integrals 44
4. Inequalities 46
5. Modes of Convergence 51
Chapter 4. Derivatives via Signed Measures
1. Decomposition of Signed Measures 61
2. The Radon Nikodym Theorem 66
3. Lebesgue s Theorem 70
4. The Fundamental Theorem of Calculus 74
Chapter 5. Measures and Processes on Products
1. Finite Dimensional Product Spaces 79
2. Random Vectors on (fi, A, P) 84
3. Countably Infinite Product Probability Spaces 86
4. Random Elements and Processes on (fl. A, P) 90
Chapter 6. General Topology and Hilbert Space
1. General Topology 95
2. Metric Spaces 101
3. Hilbert Space 104
x CONTENTS
Chapter 7. Distribution and Quantile Functions
1. Character of Distribution Functions 107
2. Properties of Distribution Functions 110
3. The Quantile Transformation 111
4. Integration by Parts Applied to Moments 115
5. Important Statistical Quantities 119
6. Infinite Variance 123
7. Slowly Varying Partial Variance 128
8. Specific Tail Relationships 135
9. Regularly Varying Functions 138
10. Some Winsorized Variance Comparisons 142
11. Inequalities for Winsorized Quantile Functions 149
Chapter 8. Independence and Conditional Distributions
1. Independence 153
2. The Tail a Field 157
3. Uncorrelated Random Variables 159
4. Basic Properties of Conditional Expectation 160
5. Regular Conditional Probability 170
6. Conditional Expectations as Projections 176
Chapter 9. Special Distributions
1. Elementary Probability 181
2. Distribution Theory for Statistics 189
3. Linear Algebra Applications 193
4. The Multivariate Normal Distribution 201
Chapter 10. WLLN, SLLN, LIL, and Series
0. Introduction 205
1. Borel Cantelli and Kronecker Lemmas 206
2. Truncation, WLLN, and Review of Inequalities 208
3. Maximal Inequalities and Symmetrization 212
4. The Classical Laws of Large Numbers, LLNs 217
5. Applications of the Laws of Large Numbers 225
6. General Moment Estimation 228
7. Law of the Iterated Logarithm 237
8. Strong Markov Property for Sums of IID RVs 241
9. Convergence of Series of Independent RVs 243
10. Martingales 248
11. Maximal Inequalities, Some with f Boundaries 249
12. A Uniform SLLN 254
CONTENTS xi
Chapter 11. Convergence in Distribution
1. Stein s Method for CLTs 257
2. Winsorization and Truncation 266
3. Identically Distributed RVs 271
4. Bootstrapping 276
5. Bootstrapping with Slowly Increasing Trimming 278
6. Examples of Limiting Distributions 281
7. Classical Convergence in Distribution 290
8. Limit Determining Classes of Functions 294
Chapter 12. Brownian Motion and Empirical Processes
1. Special Spaces 297
2. Existence of Processes on (C, C) and (£ , T ) 300
3. Brownian Motion and Brownian Bridge 304
4. Stopping Times 307
5. Strong Markov Property 310
6. Embedding a RV in Brownian Motion 313
7. Barrier Crossing Probabilities 316
8. Embedding the Partial Sum Process 320
9. Other Properties of Brownian Motion 325
10. Various Empirical Processes 327
11. Inequalities for the Various Empirical Processes 335
12. Applications 340
Chapter 13. Characteristic Functions
1. Basic Results, with Derivation of Common Chfs 343
2. Uniqueness and Inversion 348
3. The Continuity Theorem 352
4. Elementary Complex and Fourier Analysis 354
5. Esseen s Lemma 360
6. Distributions on Grids 363
7. Conditions for 4 to Be a Characteristic Function 365
Chapter 14. CLTs via Characteristic Functions
0. Introduction 367
1. Basic Limit Theorems 368
2. Variations on the Classical CLT 373
3. Local Limit Theorems 382
4. Gamma Approximation 385
5. Edgeworth Expansions 393
6. Approximating the Distribution of h(Xn) 399
xii CONTENTS
Chapter 15. Infinitely Divisible and Stable Distributions
1. Infinitely Divisible Distributions 401
2. Stable Distributions 409
3. Characterizing Stable Laws 412
4. The Domain of Attraction of a Stable Law 414
Chapter 16. Asymptotics via Empirical Proceses
0. Introduction 417
1. Trimmed and Winsorized Means 418
2. Linear Rank Statistics and Finite Sampling 428
3. The Bootstrap 434
4. L Statistics 439
Chapter 17. Asymptotics via Stein s Approach
1. U Statistics 451
2. Hoeffding s Combinatorial CLT 460
Chapter 18. Martingales
1. Basic Technicalities for Martingales 469
2. Simple Optional Sampling Theorem 474
3. The Submartingale Convergence Theorem 475
4. Applications of the S mg Convergence Theorem 483
5. Decomposition of a Submartingale Sequence 489
6. Optional Sampling 494
7. Applications of Optional Sampling 501
8. Introduction to Counting Process Martingales 503
9. Doob Meyer Submartingale Decomposition 513
10. Predictable Processes and /0 H dM Martingales 518
11. The Basic Censored Data Martingale 524
12. CLTs for Dependent RVs 531
Chapter 19. Convergence in Law on Metric Spaces
1. Convergence in Distribution on Metric Spaces 533
2. Metrics for Convergence in Distribution 542
Appendix A. Distribution Summaries
1. The Gamma and Digamma Functions 548
2. Maximum Likelihood Estimators and Moments 553
3. Examples of Statistical Models 557
4. Asymptotics of Maximum Likelihood Estimation 565
References 570
Index 575
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-search | 519.2 519.2 21 |
| dewey-sort | 3519.2 |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| indexdate | 2024-07-09T18:42:20Z |
| institution | BVB |
| isbn | 0387989536 |
| language | English |
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| spelling | Shorack, Galen R. 1939- Verfasser (DE-588)122259122 aut Probability for statisticians Galen R. Shorack New York [u.a.] Springer 2000 XVII, 585 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Maattheorie gtt Probabilidade (textos elementares) larpcal Probabilités Waarschijnlijkheid (statistiek) gtt Probabilities Wahrscheinlichkeit (DE-588)4137007-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Wahrscheinlichkeit (DE-588)4137007-7 s Statistik (DE-588)4056995-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009024981&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009024981&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Buchcover |
| spellingShingle | Shorack, Galen R. 1939- Probability for statisticians Maattheorie gtt Probabilidade (textos elementares) larpcal Probabilités Waarschijnlijkheid (statistiek) gtt Probabilities Wahrscheinlichkeit (DE-588)4137007-7 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4137007-7 (DE-588)4056995-0 |
| title | Probability for statisticians |
| title_auth | Probability for statisticians |
| title_exact_search | Probability for statisticians |
| title_full | Probability for statisticians Galen R. Shorack |
| title_fullStr | Probability for statisticians Galen R. Shorack |
| title_full_unstemmed | Probability for statisticians Galen R. Shorack |
| title_short | Probability for statisticians |
| title_sort | probability for statisticians |
| topic | Maattheorie gtt Probabilidade (textos elementares) larpcal Probabilités Waarschijnlijkheid (statistiek) gtt Probabilities Wahrscheinlichkeit (DE-588)4137007-7 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Maattheorie Probabilidade (textos elementares) Probabilités Waarschijnlijkheid (statistiek) Probabilities Wahrscheinlichkeit Statistik |
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