Statistical inference for ergodic diffusion processes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2004
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| Series: | Springer series in statistics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz.: S. 467-478 |
| Physical Description: | XIII, 481 S. |
| ISBN: | 1852337591 |
Staff View
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Record in the Search Index
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| adam_text | YURY A. KUTOYANTS STATISTICAL INFERENCE FOR ERGODIC DIFFUSION PROCESSES
SPRINGER CONTENTS PREFACE VII INTRODUCTION 1 1 DIFFUSION PROCESSES AND
STATISTICAL PROBLEMS 17 1.1 STOCHASTIC DIFFERENTIAL EQUATION 17 1.1.1
STOCHASTIC INTEGRAL 17 1.1.2 DIFFUSION PROCESS 23 1.1.3 LOCAL TIME 27
1.1.4 LIKELIHOOD RATIO 33 1.2 LIMIT THEOREMS 39 1.2.1 LAW OF LARGE
NUMBERS 39 1.2.2 CENTRAL LIMIT THEOREM 43 1.3 STATISTICAL INFERENCE 50
1.3.1 PARAMETER ESTIMATION 51 1.3.2 NONPARAMETRIC ESTIMATION 83 1.3.3
HYPOTHESES TESTING 103 2 PARAMETER ESTIMATION ILL 2.1 MAXIMUM LIKELIHOOD
AND BAYESIAN ESTIMATORS ILL 2.1.1 LOWER BOUND 112 2.1.2 MAXIMUM
LIKELIHOOD ESTIMATOR 116 2.1.3 BAYESIAN ESTIMATORS 129 2.1.4 EXAMPLES
134 2.2 MINIMUM DISTANCE ESTIMATORS 139 2.2.1 FIRST MDE 140 2.2.2
EXAMPLES -. 147 2.2.3 SECOND MDE 149 2.3 TRAJECTORY FITTING ESTIMATOR
158 . 2.3.1 PROPERTIES OF TFE 159 2.3.2 EXAMPLE 169 CONTENTS 2.4
ESTIMATOR OF THE METHOD OF MOMENTS 170 2.4.1 PROPERTIES OF EMM 171 2.4.2
EXAMPLES 174 2.5 ONE-STEP MLE 176 2.5.1 PARAMETER ESTIMATION 176 2.5.2
DISTRIBUTION FUNCTION ESTIMATION 182 2.5.3 DENSITY ESTIMATION 186 2.6
MISCELLANEOUS 190 2.6.1 NO TRUE MODEL 191 2.6.2 TOO MANY TRUE MODELS 204
2.6.3 NULL FISHER INFORMATION 208 2.6.4 OPTIMAL OBSERVATION WINDOW 211
2.6.5 ASYMPTOTIC EXPANSIONS 216 2.6.6 RECURSIVE ESTIMATION 223 SPECIAL
MODELS 227 3.1 PARTIALLY OBSERVED SYSTEMS 227 3.1.1 KALMAN-BUCY FILTER
228 3.1.2 PROPERTIES OF ESTIMATORS 230 3.1.3 EXAMPLES 236 3.2 CUSP
ESTIMATION 238 3.2.1 MODEL 238 3.2.2 PROPERTIES OF ESTIMATORS 238 3.2.3
DISCUSSIONS 251 3.3 DELAY ESTIMATION 253 3.3.1 SDE WITH DELAY 253 3.3.2
PROPERTIES OF MLE AND BE 255 3.3.3 DISCUSSION 268 3.4 CHANGE-POINT
ESTIMATION 269 3.4.1 SIMPLE SWITCHING 269 3.4.2 GENERAL CASE 274 3.4.3
EXAMPLES 282 3.4.4 DISCUSSION 283 3.4.5 CONTAMINATED SWITCHING 290 3.5
NON ERGODIC PROCESSES 293 3.5.1 NULL RECURRENT PROCESS 294 3.5.2
POLYNOMIAL GROWTH PROCESS 302 3.5.3 EXPONENTIAL GROWTH PROCESS 303
NONPARAMETRIC ESTIMATION 309 4.1 DISTRIBUTION FUNCTION ESTIMATION 309
4.1.1 LOWER BOUND 310 4.1.2 EDF !. 315 4.1.3 EXAMPLE 318 4.1.4 OTHER
METRICS 321 CONTENTS XIII 4.2 DENSITY ESTIMATION 322 4.2.1 LOWER BOUND
322 4.2.2 LOCAL-TIME ESTIMATOR 326 4.2.3 OTHER ESTIMATORS 334 4.3
SEMIPARAMETRIC ESTIMATION 337 4.3.1 LOWER BOUND 338 4.3.2 EMPIRICAL
ESTIMATOR 341 4.3.3 REMARKS 343 4.3.4 INTEGRAL TYPE RISK 345 4.4 DENSITY
DERIVATIVE ESTIMATION 351 4.4.1 GLOBAL RISK 353 4.4.2 LOCAL RISK 373 4.5
TREND COEFFICIENT ESTIMATION 383 4.5.1 OPTIMAL RATE 384 4.5.2 LOWER
BOUND 389 4.5.3 EFFICIENT ESTIMATOR 390 4.5.4 ADAPTIVE ESTIMATOR 393 4.6
SECOND ORDER EFFICIENCY 396 4.6.1 PROBLEM 396 4.6.2 LOWER BOUND 399
4.6.3 EFFICIENT ESTIMATOR 408 4.6.4 DISCUSSION 417 5 HYPOTHESES TESTING
421 5.1 SIMPLE HYPOTHESIS AND ALTERNATIVE 421 5.1.1 LARGE DEVIATIONS
PRINCIPLE 422 5.1.2 ASYMPTOTIC BEHAVIOR OF ERRORS 424 5.2 ONE-SIDED
PARAMETRIC ALTERNATIVES 427 5.2.1 SCORE FUNCTION TEST 430 5.2.2
LIKELIHOOD RATIO AND BAYESIAN TESTS 438 5.3 ONE-SIDED NONPARAMETRIC
ALTERNATIVE 451 5.3.1 LOCAL ALTERNATIVES 451 5.3.2 ASYMPTOTICALLY
OPTIMAL TEST 453 5.4 GOODNESS-OF-FIT TEST 458 HISTORICAL REMARKS 461
REFERENCES 467 INDEX 479
|
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| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV019676137 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:03:33Z |
| institution | BVB |
| isbn | 1852337591 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013004237 |
| oclc_num | 635025889 |
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| owner_facet | DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-11 DE-83 |
| physical | XIII, 481 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spelling | Kutoyants, Yu. A. 1946- Verfasser (DE-588)172202272 aut Statistical inference for ergodic diffusion processes Yury A. Kutoyants London [u.a.] Springer 2004 XIII, 481 S. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Literaturverz.: S. 467-478 Parameterschätzung (DE-588)4044614-1 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Diffusionsprozess (DE-588)4274463-5 gnd rswk-swf Diffusionsprozess (DE-588)4274463-5 s Ergodentheorie (DE-588)4015246-7 s Parameterschätzung (DE-588)4044614-1 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013004237&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kutoyants, Yu. A. 1946- Statistical inference for ergodic diffusion processes Parameterschätzung (DE-588)4044614-1 gnd Ergodentheorie (DE-588)4015246-7 gnd Diffusionsprozess (DE-588)4274463-5 gnd |
| subject_GND | (DE-588)4044614-1 (DE-588)4015246-7 (DE-588)4274463-5 |
| title | Statistical inference for ergodic diffusion processes |
| title_auth | Statistical inference for ergodic diffusion processes |
| title_exact_search | Statistical inference for ergodic diffusion processes |
| title_full | Statistical inference for ergodic diffusion processes Yury A. Kutoyants |
| title_fullStr | Statistical inference for ergodic diffusion processes Yury A. Kutoyants |
| title_full_unstemmed | Statistical inference for ergodic diffusion processes Yury A. Kutoyants |
| title_short | Statistical inference for ergodic diffusion processes |
| title_sort | statistical inference for ergodic diffusion processes |
| topic | Parameterschätzung (DE-588)4044614-1 gnd Ergodentheorie (DE-588)4015246-7 gnd Diffusionsprozess (DE-588)4274463-5 gnd |
| topic_facet | Parameterschätzung Ergodentheorie Diffusionsprozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013004237&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kutoyantsyua statisticalinferenceforergodicdiffusionprocesses |