Statistical inference for diffusion type processes:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
London [u.a.]
Arnold [u.a.]
1999
|
| Schriftenreihe: | Kendall's library of statistics
8 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008919832&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVI, 349 S. |
| ISBN: | 034074149X 9780470711125 |
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Datensatz im Suchindex
| _version_ | 1819368288439762944 |
|---|---|
| adam_text | IMAGE 1
STATISTICAL INFERENCE FOR
DIFFUSION TYPE PROCESSES
B.L.S. PRAKASA RAO INDIAN STATISTICAL INSTITUTE, NEW DELHI
ARNOLD A MEMBER OF THE HODDER HEADLINE GROUP LONDON * SYDNEY * AUCKLAND
CO-PUBLISHED IN THE USA BY OXFORD UNIVERSITY PRESS INC., NEW YORK
IMAGE 2
CONTENTS
PREFACE XI
INTRODUCTORY NOTES XIII
1 DIFFUSION TYPE PROCESSES 1
1.1 INTRODUCTION 1
1.2 DIFFUSION TYPE PROCESSES 2
1.2.1 DIFFUSION PROCESSES 2
1.2.2 DIFFUSION TYPE PROCESSES 10
2 PARAMETRIC INFERENCE FOR DIFFUSION TYPE PROCESSES FROM CONTINUOUS
PATHS 15 2.1 INTRODUCTION 15
2.2 MAXIMUM LIKELIHOOD METHOD FOR THE ESTIMATION OF THE DRIFT PARAMETER
16 2.2.1 DIFFUSION PROCESSES 16
2.2.2 DIFFUSION TYPE PROCESSES 28
2.2.3 CRAM6R-RAO LOWER BOUND 28
2.3 MINIMUM CONTRAST METHOD FOR THE ESTIMATION OF THE DRIFT PARAMETER 50
2.4 MAXIMUM PROBABILITY ESTIMATION FOR THE DRIFT PARAMETER 55
2.4.1 EXISTENCE OF A VF-CONSISTENT ESTIMATOR FOR 0 58
2.4.2 EXISTENCE OF A MAXIMUM PROBABILITY ESTIMATOR 60
2.4.3 ASYMPTOTIC NORMALITY OF THE MAXIMUM PROBABILITY ESTIMATOR 62
2.5 BAYES METHOD FOR THE ESTIMATION OF THE DRIFT PARAMETER 64
2.6 MINIMUM DISTANCE METHOD FOR THE ESTIMATION OF THE DRIFT PARAMETER 70
2.6.1 LOO-NORM (MDE) 71
2.6.2 L 2 -NORM (MDE) 76
2.6.3 LI-NORM (MDE) 83
2.7 M-ESTIMATION METHOD FOR THE ESTIMATION OF DRIFT PARAMETER 84
2.7.1 ASYMPTOTIC BEHAVIOR OF M-ESTIMATORS 86
2.7.2 LOCAL ASYMPTOTIC MIXED NORMALITY 88
2.7.3 ESTIMATION BY A MISSPECIFIED MODEL 93
2.8 RECURSIVE ESTIMATION 97
2.8.1 MLE EVOLUTION EQUATION 98
2.9 SEQUENTIAL ESTIMATION 99
IMAGE 3
VIII CONTENTS
2.9.1 MAXIMUM LIKELIHOOD ESTIMATION 102
2.10 ESTIMATION FROM INCOMPLETE OBSERVATIONS 110
2.10.1 ASYMPTOTIC SUFFICIENCY 110
2.10.2 EXAMPLES OF INCOMPLETE DATA 116
2.11 ESTIMATION FROM FIRST HITTING TIMES 119
2.11.1 MINIMUM CONTRAST ESTIMATION 120
2.11.2 CONSISTENCY 124
2.11.3 ASYMPTOTIC NORMALITY 125
3 PARAMETRIC INFERENCE FOR DIFFUSION TYPE PROCESSES FROM SAMPLED DATA
131 3.1 INTRODUCTION 131
3.2 ESTIMATION BY THE LEAST-SQUARES METHOD 133
3.3 ESTIMATION BY THE MAXIMUM LIKELIHOOD METHOD 147
3.4 OTHER METHODS OF ESTIMATION VIA NUMERICAL APPROXIMATION SCHEMES 153
3.4.1 PSEUDO-LIKELIHOOD APPROACH 153
3.4.2 GENERALIZED METHOD OF MOMENTS 169
3.4.3 COMPARISON OF DISCRETIZATION METHODS 171
3.5 ESTIMATION VIA MARTINGALE ESTIMATING FUNCTIONS 172
3.5.1 LINEAR ESTIMATING FUNCTIONS 172
3.5.2 CONSISTENCY AND ASYMPTOTIC NORMALITY 178
3.5.3 QUADRATIC ESTIMATING FUNCTIONS 179
3.5.4 ESTIMATING FUNCTIONS BASED ON EIGENFUNCTIONS 182
3.6 ESTIMATION OF THE DIFFUSION PARAMETER 189
3.6.1 DETERMINISTIC SAMPLING 189
3.6.2 RANDOM SAMPLING 195
3.6.3 ESTIMATION BY APPROXIMATION OF THE TRANSITION FUNCTION 199
3.7 SIMULATION-BASED ESTIMATION METHODS 211
3.7.1 INDIRECT INFERENCE FOR DIFFUSION PROCESSES 213
3.7.2 QUASI-INDIRECT INFERENCE FOR DIFFUSION PROCESSES 214
3.7.3 ESTIMATION BY SIMULATED MOMENT METHODS 217
3.7.4 ESTIMATION BY THE METHOD OF MINIMUM CHI-SQUARED 219
3.8 BAYESIAN INFERENCE 221
4 NONPARAMETRIC INFERENCE FOR DIFFUSION TYPE PROCESSES FROM CONTINUOUS
SAMPLE PATHS 225
4.1 INTRODUCTION 225
4.2 STATIONARY DIFFUSION MODEL 225
4.2.1 CENTRAL LIMIT THEOREM 227
4.2.2 ESTIMATION BY THE METHOD OF DELTA FAMILIES 227
4.2.3 ESTIMATION OF THE DRIFT FOR DIFFUSION PROCESSES BY OTHER METHODS
230 4.2.4 EFFICIENT DENSITY ESTIMATION 239
4.3 NONSTATIONARY DIFFUSION MODEL 242
4.3.1 ESTIMATION OF THE DRIFT BY THE KERNEL METHOD 242
4.3.2 ESTIMATION OF THE DRIFT BY THE METHOD OF SIEVES 244
4.4 LINEAR STOCHASTIC SYSTEMS 248
4.4.1 ESTIMATION UNDER OBSERVATION SCHEME I 251
4.4.2 ESTIMATION UNDER OBSERVATION SCHEME II 255
IMAGE 4
CONTENTS
IX
5 NONPARAMETRIC INFERENCE FOR DIFFUSION TYPE PROCESSES FROM SAMPLED DATA
257 5.1 INTRODUCTION 257
5.2 NONPARAMETRIC INFERENCE FROM SAMPLED DATA FOR GENERAL STOCHASTIC
PROCESSES 257 5.3 ESTIMATION OF THE DRIFT COEFFICIENT 260
5.4 ESTIMATION OF THE DIFFUSION COEFFICIENT 264
5.4.1 METHOD OF NEAREST NEIGHBORS 265
5.4.2 METHOD OFWAVELETS 268
5.4.3 ESTIMATION BY MATCHING THE DRIFT AND THE DIFFUSION TO THE MARGINAL
DENSITY 273
5.4.4 ESTIMATION BY MINIMIZING L2-DISTANCE 277
5.4.5 EFFICIENT ESTIMATION UNDER THE L^-LOSS FUNCTION 279
6 APPLICATIONS TO STOCHASTIC MODELING 283
6.1 INTRODUCTION 283
6.2 MATHEMATICAL FINANCE 283
6.2.1 MODELS FOR PRICING, INTEREST RATES AND RISK 283
6.3 FOREST MANAGEMENT 291
6.4 MARKET POLICY 292
7 NUMERICAL APPROXIMATION METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS
295 7.1 INTRODUCTION 295
7.2 APPROXIMATION OF A STOCHASTIC DIFFERENTIAL EQUATION 296
7.3 EFFECTS OF DISCRETIZATION IN ESTIMATION FOR DIFFUSION PROCESSES 299
7.4 UNIFORM APPROXIMATION FOR STOCHASTIC INTEGRALS OF FUNCTIONS OF A
SOLUTION OF A STOCHASTIC DIFFERENTIAL EQUATION 304
APPENDIX A UNIFORM ERGODIC THEOREM 305
APPENDIX B STOCHASTIC INTEGRATION AND LIMIT THEOREMS FOR STOCHASTIC
INTEGRALS 307 B. 1 STOCHASTIC INTEGRALS WITH RESPECT TO A WIENER PROCESS
307
B.2 INTERCHANGING STOCHASTIC INTEGRATION AND ORDINARY DIFFERENTATION 316
B.3 FUBINI TYPE THEOREM FOR STOCHASTIC INTEGRALS 319
B.4 SUFFICIENT CONDITIONS FOR THE DIFFERENTIABILITY OF AN ITO STOCHASTIC
INTEGRAL 319
APPENDIX C WAVELETS 321
APPENDIX D GRONWALL-BELLMAN TYPE LEMMA 325
REFERENCES 327
AUTHOR INDEX 343
SUBJECT INDEX 347
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV013095883 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:41:13Z |
| institution | BVB |
| isbn | 034074149X 9780470711125 |
| language | English |
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| physical | XVI, 349 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Arnold [u.a.] |
| record_format | marc |
| series | Kendall's library of statistics |
| series2 | Kendall's library of statistics |
| spellingShingle | Prakasa Rao, Bhagavatula L. S. 1942- Statistical inference for diffusion type processes Kendall's library of statistics Diffusie (natuurwetenschappen) gtt Mathematical statistics Probabilities Statistische analyse gtt Stochastische processen gtt Diffusion processes Diffusion (DE-588)4012277-3 gnd Inferenzstatistik (DE-588)4247120-5 gnd |
| subject_GND | (DE-588)4012277-3 (DE-588)4247120-5 |
| title | Statistical inference for diffusion type processes |
| title_auth | Statistical inference for diffusion type processes |
| title_exact_search | Statistical inference for diffusion type processes |
| title_full | Statistical inference for diffusion type processes B. L. S. Prakasa Rao |
| title_fullStr | Statistical inference for diffusion type processes B. L. S. Prakasa Rao |
| title_full_unstemmed | Statistical inference for diffusion type processes B. L. S. Prakasa Rao |
| title_short | Statistical inference for diffusion type processes |
| title_sort | statistical inference for diffusion type processes |
| topic | Diffusie (natuurwetenschappen) gtt Mathematical statistics Probabilities Statistische analyse gtt Stochastische processen gtt Diffusion processes Diffusion (DE-588)4012277-3 gnd Inferenzstatistik (DE-588)4247120-5 gnd |
| topic_facet | Diffusie (natuurwetenschappen) Mathematical statistics Probabilities Statistische analyse Stochastische processen Diffusion processes Diffusion Inferenzstatistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008919832&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010165867 |
| work_keys_str_mv | AT prakasaraobhagavatulals statisticalinferencefordiffusiontypeprocesses |