Expansions and asymptotics for statistics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fl. [u.a.]
CRC Press [u.a.]
2010
|
| Series: | Monographs on statistics and applied probability
115 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 343 S. Ill., graph. Darst. |
| ISBN: | 9781584885900 1584885904 |
Staff View
MARC
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| 245 | 1 | 0 | |a Expansions and asymptotics for statistics |c Christopher G. Small |
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Record in the Search Index
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|---|---|
| adam_text | IMAGE 1
CONTENTS
PREFACE XI
1 INTRODUCTION 1
1.1 EXPANSIONS AND APPROXIMATIONS 1
1.2 THE ROLE OF ASYMPTOTICS 3
1.3 MATHEMATICAL PRELIMINARIES 4
1.4 TWO COMPLEMENTARY APPROACHES 16
1.5 PROBLEMS 18
2 GENERAL SERIES METHODS 23
2.1 A QUICK OVERVIEW 23
2.2 POWER SERIES 24
2.3 ENVELOPING SERIES 40
2.4 ASYMPTOTIC SERIES 47
2.5 SUPERASYMPTOTIC AND HYPERASYMPTOTIC SERIES 63
2.6 ASYMPTOTIC SERIES FOR LARGE SAMPLES 66
2.7 GENERALISED ASYMPTOTIC EXPANSIONS 68
2.8 NOTES 69
2.9 PROBLEMS 69
3 PADE APPROXIMANTS AND CONTINUED FRACTIONS 75
3.1 THE PADE TABLE 75
3.2 PADE APPROXIMATIONS FOR THE EXPONENTIAL FUNCTION 79
IMAGE 2
3.3 TWO APPLICATIONS 81
3.4 CONTINUED FRACTION EXPANSIONS 85
3.5 A CONTINUED FRACTION FOR THE NORMAL DISTRIBUTION 88
3.6 APPROXIMATING TRANSFORMS AND OTHER INTEGRALS 90
3.7 MULTIVARIATE EXTENSIONS 92
3.8 NOTES 93
3.9 PROBLEMS 94
4 THE DELTA METHOD AND ITS EXTENSIONS 99
4.1 INTRODUCTION TO THE DELTA METHOD 99
4.2 PRELIMINARY RESULTS 100
4.3 THE DELTA METHOD FOR MOMENTS 103
4.4 USING THE DELTA METHOD IN MAPLE 108
4.5 ASYMPTOTIC BIAS 109
4.6 VARIANCE STABILISING TRANSFORMATIONS 111
4.7 NORMALISING TRANSFORMATIONS 114
4.8 PARAMETER TRANSFORMATIONS 116
4.9 FUNCTIONS OF SEVERAL VARIABLES 119
4.10 RATIOS OF AVERAGES 119
4.11 THE DELTA METHOD FOR DISTRIBUTIONS 121
4.12 THE VON MISES CALCULUS 123
4.13 OBSTACLES AND OPPORTUNITIES: ROBUSTNESS 134
4.14 PROBLEMS 137
5 OPTIMALITY AND LIKELIHOOD ASYMPTOTICS 143
5.1 HISTORICAL OVERVIEW 143
5.2 THE ORGANISATION OF THIS CHAPTER 151
5.3 THE LIKELIHOOD FUNCTION AND ITS PROPERTIES 152
5.4 CONSISTENCY OF MAXIMUM LIKELIHOOD 159
5.5 ASYMPTOTIC NORMALITY OF MAXIMUM LIKELIHOOD 161
IMAGE 3
UUIN JL VLN 1 S IX
5.6 ASYMPTOTIC COMPARISON OF ESTIMATORS 164
5.7 LOCAL ASYMPTOTICS 171
5.8 LOCAL ASYMPTOTIC NORMALITY 177
5.9 LOCAL ASYMPTOTIC MINIMAXITY 181
5.10 VARIOUS EXTENSIONS 185
5.11 PROBLEMS 187
6 THE LAPLACE APPROXIMATION AND SERIES 193
6.1 A SIMPLE EXAMPLE 193
6.2 THE BASIC APPROXIMATION 195
6.3 THE STIRLING SERIES FOR FACTORIALS 200
6.4 LAPLACE EXPANSIONS IN MAPLE 201
6.5 ASYMPTOTIC BIAS OF THE MEDIAN 202
6.6 RECURRENCE PROPERTIES OF RANDOM WALKS 205
6.7 PROOFS OF THE MAIN PROPOSITIONS 207
6.8 INTEGRALS WITH THE MAXIMUM ON THE BOUNDARY 211
6.9 INTEGRALS OF HIGHER DIMENSION 212
6.10 INTEGRALS WITH PRODUCT INTEGRANDS 215
6.11 APPLICATIONS TO STATISTICAL INFERENCE 219
6.12 ESTIMATING LOCATION PARAMETERS 220
6.13 ASYMPTOTIC ANALYSIS OF BAYES ESTIMATORS 222
6.14 NOTES 223
6.15 PROBLEMS 223
7 THE SADDLE-POINT METHOD 227
7.1 THE PRINCIPLE OF STATIONARY PHASE 227
7.2 PERRON S SADDLE-POINT METHOD 229
7.3 HARMONIC FUNCTIONS AND SADDLE-POINT GEOMETRY 234
7.4 DANIELS SADDLE-POINT APPROXIMATION 238
7.5 TOWARDS THE BARNDORFF-NIELSEN FORMULA 241
IMAGE 4
X CONTENTS
7.6 SADDLE-POINT METHOD FOR DISTRIBUTION FUNCTIONS 251
7.7 SADDLE-POINT METHOD FOR DISCRETE VARIABLES 253
7.8 RATIOS OF SUMS OF RANDOM VARIABLES 254
7.9 DISTRIBUTIONS OF M-ESTIMATORS 256
7.10 THE EDGEWORTH EXPANSION 258
7.11 MEAN, MEDIAN AND MODE 262
7.12 HAYMAN S SADDLE-POINT APPROXIMATION 263
7.13 THE METHOD OF DARBOUX 268
7.14 APPLICATIONS TO COMMON DISTRIBUTIONS 269
7.15 PROBLEMS 274
8 SUMMATION OF SERIES 279
8.1 ADVANCED TESTS FOR SERIES CONVERGENCE 279
8.2 CONVERGENCE OF RANDOM SERIES 285
8.3 APPLICATIONS IN PROBABILITY AND STATISTICS 286
8.4 EULER-MACLAURIN SUM FORMULA 291
8.5 APPLICATIONS OF THE EULER-MACLAURIN FORMULA 295
8.6 ACCELERATING SERIES CONVERGENCE 297
8.7 APPLICATIONS OF ACCELERATION METHODS 309
8.8 COMPARING ACCELERATION TECHNIQUES 313
8.9 DIVERGENT SERIES 314
8.10 PROBLEMS 316
9 GLOSSARY OF SYMBOLS 321
10 USEFUL LIMITS, SERIES AND PRODUCTS 325
REFERENCES 327
INDEX 331
|
| any_adam_object | 1 |
| author | Small, Christopher G. 1956- |
| author_GND | (DE-588)112053807 |
| author_facet | Small, Christopher G. 1956- |
| author_role | aut |
| author_sort | Small, Christopher G. 1956- |
| author_variant | c g s cg cgs |
| building | Verbundindex |
| bvnumber | BV036610001 |
| ctrlnum | (OCoLC)845710224 (DE-599)GBV619778172 |
| 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 |
| format | Book |
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| id | DE-604.BV036610001 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:44:07Z |
| institution | BVB |
| isbn | 9781584885900 1584885904 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020530286 |
| oclc_num | 845710224 |
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| owner | DE-634 DE-83 |
| owner_facet | DE-634 DE-83 |
| physical | XIV, 343 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | CRC Press [u.a.] |
| record_format | marc |
| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Small, Christopher G. 1956- Verfasser (DE-588)112053807 aut Expansions and asymptotics for statistics Christopher G. Small Boca Raton, Fl. [u.a.] CRC Press [u.a.] 2010 XIV, 343 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 115 Asymptotic distribution (Probability theory) Asymptotic expansions Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Asymptotische Verteilung (DE-588)4739185-6 gnd rswk-swf Asymptotische Verteilung (DE-588)4739185-6 s DE-604 Asymptotische Entwicklung (DE-588)4112609-9 s Monographs on statistics and applied probability 115 (DE-604)BV002494005 115 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020530286&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Small, Christopher G. 1956- Expansions and asymptotics for statistics Monographs on statistics and applied probability Asymptotic distribution (Probability theory) Asymptotic expansions Asymptotische Entwicklung (DE-588)4112609-9 gnd Asymptotische Verteilung (DE-588)4739185-6 gnd |
| subject_GND | (DE-588)4112609-9 (DE-588)4739185-6 |
| title | Expansions and asymptotics for statistics |
| title_auth | Expansions and asymptotics for statistics |
| title_exact_search | Expansions and asymptotics for statistics |
| title_full | Expansions and asymptotics for statistics Christopher G. Small |
| title_fullStr | Expansions and asymptotics for statistics Christopher G. Small |
| title_full_unstemmed | Expansions and asymptotics for statistics Christopher G. Small |
| title_short | Expansions and asymptotics for statistics |
| title_sort | expansions and asymptotics for statistics |
| topic | Asymptotic distribution (Probability theory) Asymptotic expansions Asymptotische Entwicklung (DE-588)4112609-9 gnd Asymptotische Verteilung (DE-588)4739185-6 gnd |
| topic_facet | Asymptotic distribution (Probability theory) Asymptotic expansions Asymptotische Entwicklung Asymptotische Verteilung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020530286&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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