Asymptotic theory of statistical inference for time series:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2000
|
| Series: | Springer series in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 619 - 648 |
| Physical Description: | XVII, 661 S. 24 cm |
| ISBN: | 0387950397 |
Staff View
MARC
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| 100 | 1 | |a Taniguchi, Masanobu |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Asymptotic theory of statistical inference for time series |c Masanobu Taniguchi ; Yoshihide Kakizawa |
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Record in the Search Index
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| adam_text | IMAGE 1
MASANOBU TANIGUCHI
YOSHIHIDE KAKIZAWA
ASYMPTOTIC THEORY
OF STATISTICAL INFERENCE FOR TIME SERIES
WITH LOILLUSTRATIONS
SPRINGER
IMAGE 2
CONTENTS
PREFACE VII
NOTATION XV
1 ELEMENTS OF STOCHASTIC PROCESSES 1
1.1 INTRODUCTION 1
1.2 STOCHASTIC PROCESSES 1
1.3 LIMIT THEOREMS 17
PROBLEMS 28
2 LOCAL ASYMPTOTIC NORMALITY FOR STOCHASTIC PROCESSES 31
2.1 GENERAL RESULTS FOR LOCAL ASYMPTOTIC NORMALITY 31
2.2 LOCAL ASYMPTOTIC NORMALITY FOR LINEAR PROCESSES 37
PROBLEMS 48
3 ASYMPTOTIC THEORY OF ESTIMATION AND TESTING FOR STOCHASTIC PROCESSES
51
3.1 ASYMPTOTIC THEORY OF ESTIMATION AND TESTING FOR LINEAR PROCESSES 52
3.1.1 ASYMPTOTIC THEORY BASED ON A GAUSSIAN LIKELIHOOD 52 3.1.2
ASYMPTOTIC THEORY OF ESTIMATION AND TESTING BASED ON LAN RESULTS 63
3.2 ASYMPTOTIC THEORY FOR NONLINEAR STOCHASTIC MODELS . . .. 79
3.2.1 NONLINEAR MODELS 79
IMAGE 3
XII CONTENTS
3.2.2 PROBABILITY STRUCTURE OF NONLINEAR MODELS 85
3.2.3 STATISTICAL TESTING AND ESTIMATION THEORY FOR NONLINEAR MODELS 92
3.2.4 ASYMPTOTIC THEORY BASED ON THE LAN PROPERTY . . 103 3.2.5 MODEL
SELECTION PROBLEMS 109
3.2.6 NONERGODIC MODELS 115
3.3 ASYMPTOTIC THEORY FOR CONTINUOUS TIME PROCESSES 121
3.3.1 STOCHASTIC INTEGRALS AND DIFFUSION PROCESSES 122
3.3.2 ASYMPTOTIC THEORY FOR DIFFUSION PROCESSES 129
3.3.3 DIFFUSION PROCESSES AND AUTOREGRESSIONS WITH ROOTS NEAR UNITY 140
3.3.4 CONTINUOUS TIME ARMA PROCESSES 149
3.3.5 ASYMPTOTIC THEORY FOR POINT PROCESSES 152
PROBLEMS 163
4 HIGHER ORDER ASYMPTOTIC THEORY FOR STOCHASTIC PROCESSES 167
4.1 INTRODUCTION TO HIGHER ORDER ASYMPTOTIC THEORY 168
4.2 VALID ASYMPTOTIC EXPANSIONS 187
4.3 HIGHER ORDER ASYMPTOTIC ESTIMATION THEORY FOR DISCRETE TIME
PROCESSES IN VIEW OF STATISTICAL DIFFERENTIAL GEOMETRY 212 4.4 HIGHER
ORDER ASYMPTOTIC THEORY FOR CONTINUOUS TIME PROCESSES 234
4.5 HIGHER ORDER ASYMPTOTIC THEORY FOR TESTING PROBLEMS . . . 249 4.6
HIGHER ORDER ASYMPTOTIC THEORY FOR NORMALIZING TRANSFORMATIONS 266
4.7 GENERALIZATION OF LECAM S THIRD LEMMA AND HIGHER ORDER ASYMPTOTICS
OF ITERATIVE METHODS 277
PROBLEMS 303
5 ASYMPTOTIC THEORY FOR LONG-MEMORY PROCESSES 307
5.1 SOME ELEMENTS OF LONG-MEMORY PROCESSES 309
5.2 LIMIT THEOREMS FOR FUNDAMENTAL STATISTICS 317
5.3 ESTIMATION AND TESTING THEORY FOR LONG-MEMORY PROCESSES 333 5.4
REGRESSION MODELS WITH LONG-MEMORY DISTURBANCES . . .. 345 5.5
SEMIPARAMETRIC ANALYSIS AND THE LAN APPROACH 371
PROBLEMS 381
6 STATISTICAL ANALYSIS BASED ON FUNCTIONALS OF SPECTRA 385
6.1 ESTIMATION OF NONLINEAR FUNCTIONALS OF SPECTRA 386
6.2 APPLICATION TO PARAMETER ESTIMATION FOR STATIONARY PROCESSES 399
6.3 ASYMPTOTICALLY EFFICIENT NONPARAMETRIC ESTIMATION OF FUNCTIONALS OF
SPECTRA IN GAUSSIAN STATIONARY PROCESSES . . 415 6.4 ROBUSTNESS IN THE
FREQUENCY DOMAIN APPROACH 424
IMAGE 4
CONTENTS XIII
6.4.1 ROBUSTNESS TO SMALL TRENDS OF LINEAR FUNCTIONALS OF A PERIODOGRAM
424
6.4.2 PEAK-INSENSITIVE SPECTRUM ESTIMATION 430
6.5 NUMERICAL EXAMPLES 455
PROBLEMS 472
7 DISCRIMINANT ANALYSIS FOR STATIONARY TIME SERIES 477
7.1 BASIC FORMULATION 478
7.2 STANDARD METHODS FOR GAUSSIAN STATIONARY PROCESSES . . .. 480 7.2.1
TIME DOMAIN METHODS 480
7.2.2 FREQUENCY DOMAIN METHODS 490
7.2.3 ADMISSIBLE LINEAR PROCEDURE: CASE OF UNEQUAL MEAN VECTORS AND
COVARIANCE MATRICES 494
7.3 DISCRIMINANT ANALYSIS FOR NON-GAUSSIAN LINEAR PROCESSES 500 7.4
NONPARAMETRIC APPROACH FOR DISCRIMINANT ANALYSIS 505
7.5 PARAMETRIC APPROACH FOR DISCRIMINANT ANALYSIS 514
7.6 DERIVATION OF SPECTRAL EXPRESSIONS TO DIVERGENCE MEASURES BETWEEN
GAUSSIAN STATIONARY PROCESSES 526
7.7 MISCELLANY 531
PROBLEMS 534
8 LARGE DEVIATION THEORY AND SADDLEPOINT APPROXIMATION FOR STOCHASTIC
PROCESSES 537
8.1 LARGE DEVIATION THEOREM 538
8.2 ASYMPTOTIC EFFICIENCY FOR GAUSSIAN STATIONARY PROCESSES: LARGE
DEVIATION APPROACH 546
8.2.1 ASYMPTOTIC THEORY OF NEYMAN-PEARSON TESTS . . . . 546 8.2.2
BAHADUR EFFICIENCY OF ESTIMATOR 551
8.2.3 STOCHASTIC COMPARISON OF TESTS 561
8.3 LARGE DEVIATION RESULTS FOR AN ORNSTEIN-UHLENBECK PROCESS 570 8.4
SADDLEPOINT APPROXIMATIONS FOR STOCHASTIC PROCESSES . . .. 578 PROBLEMS
601
APPENDIX 605
A.L MATHEMATICS 605
A.2 PROBABILITY 609
A.3 STATISTICS 617
BIBLIOGRAPHY 619
AUTHOR INDEX 649
SUBJECT INDEX 657
|
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| isbn | 0387950397 |
| language | English |
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| spelling | Taniguchi, Masanobu Verfasser aut Asymptotic theory of statistical inference for time series Masanobu Taniguchi ; Yoshihide Kakizawa New York [u.a.] Springer 2000 XVII, 661 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Literaturverz. S. 619 - 648 Processus stochastiques Stochastische processen gtt Série chronologique Tijdreeksen gtt Time-series analysis Stochastic processes Statistische Schlussweise (DE-588)4182963-3 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Asymptotische Statistik (DE-588)4203167-9 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 s Stochastischer Prozess (DE-588)4057630-9 s Statistische Schlussweise (DE-588)4182963-3 s Asymptotische Statistik (DE-588)4203167-9 s DE-604 Kakizawa, Yoshihide Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009158333&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Taniguchi, Masanobu Kakizawa, Yoshihide Asymptotic theory of statistical inference for time series Processus stochastiques Stochastische processen gtt Série chronologique Tijdreeksen gtt Time-series analysis Stochastic processes Statistische Schlussweise (DE-588)4182963-3 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd Asymptotische Statistik (DE-588)4203167-9 gnd |
| subject_GND | (DE-588)4182963-3 (DE-588)4057630-9 (DE-588)4067486-1 (DE-588)4203167-9 |
| title | Asymptotic theory of statistical inference for time series |
| title_auth | Asymptotic theory of statistical inference for time series |
| title_exact_search | Asymptotic theory of statistical inference for time series |
| title_full | Asymptotic theory of statistical inference for time series Masanobu Taniguchi ; Yoshihide Kakizawa |
| title_fullStr | Asymptotic theory of statistical inference for time series Masanobu Taniguchi ; Yoshihide Kakizawa |
| title_full_unstemmed | Asymptotic theory of statistical inference for time series Masanobu Taniguchi ; Yoshihide Kakizawa |
| title_short | Asymptotic theory of statistical inference for time series |
| title_sort | asymptotic theory of statistical inference for time series |
| topic | Processus stochastiques Stochastische processen gtt Série chronologique Tijdreeksen gtt Time-series analysis Stochastic processes Statistische Schlussweise (DE-588)4182963-3 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd Asymptotische Statistik (DE-588)4203167-9 gnd |
| topic_facet | Processus stochastiques Stochastische processen Série chronologique Tijdreeksen Time-series analysis Stochastic processes Statistische Schlussweise Stochastischer Prozess Zeitreihenanalyse Asymptotische Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009158333&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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