Abstract inference:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1981
|
| Schriftenreihe: | Wiley series in probability and mathematical statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 526 S. |
| ISBN: | 0471082678 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804117738192371712 |
|---|---|
| adam_text | Contents
INTRODUCTION 1
1 The two objects of study, 1
2 Observing general objects, 2
3 Parametric study of nonparametric problems, 5
4 General approach, 8
Notation, 9
PART 1 SOME PROBABILITY THEORY ON
ABSTRACT SPACES 13
1 Probabilistic background, 15
1 Probabilities in function spaces, 15
2 Probabilities in topological vector spaces, 24
3 Probabilities in locally compact spaces, 30
2 Geometry of stochastic processes, 37 ¦
1 Curves in Hilbert space, 37
2 Calculus of second-order processes, 46
3 Representations of processes, 54
4 Special representations, 62
5 Toeplitz theory of stationary process, 85
6 Reproducing covariance kernels, 93
PART 2 INFERENCE IN ABSTRACT SAMPLE SPACE 103
3 General inference in abstract sample space, 105
1 Likelihood ratios in abstract space, 105
2 Calculating Radon-Nikodym derivatives, 114
3 Perpendicular measures and consistent estimation, 133
vil
viii Contents
4 Linear inference, 147
1 The finite-dimensional situation, 147
2 Consistent estimation, 156
3 BLUEs for stochastic processes, 179
4 Asymptotic optimality; discrete time, 212
5 Asymptotic optimality; continuous case, 244
6 Linear inference in Banach spaces, 251
7 Selecting linear functionals for estimation, 258
5 Testing Gaussian processes, 269
1 Testing mean value functions, 269
2 Testing covariance functions, 278
3 Selecting linear functionals for testing, 290
6 Inference in Markov processes, 304
1 The infinitesimal generator as parameter, 304
2 Finite Markov chains, 307
3 Birth-and-death processes with linear growth, 317
4 Processes with independent increments, 323
5 Estimation for diffusion processes, 336
6 Likelihood estimation for some
general Markov processes, 340
PART 3 INFERENCE IN ABSTRACT PARAMETER SPACE, 345
7 Regularization in abstract parameter space, 347
1 Parametric methods for nonparametric questions, 347
2 Direct methods in abstract parameter space, 358
3 Regularization of spectral estimates, 361
4 Regularization of frequency estimates, 369
5 Regularization of sets, 373
6 General regularization, 386
8 Sieves in parameter space, 390
1 Parameter in /,-space, 390
2 Parameter in £,,-space, 395
Contents ix
3 Parameter in l2- and L2-spaces, 420
4 Parameter in C-spaces, 426
5 Parameter in a -BF-space, 442
6 Operators as parameter, 444
7 Parameter in groups, 452
8 Sets as parameters, 465
9 General Parameter Space, 469
1 General conditions for sieves, 469
2 Regularization via sieves, 472
3 Sieves in general, 478
4 Cramer-Rao s inequality in Banach spaces, 484
NOTES, 492
BIBLIOGRAPHY, 511
INDEX, 523
|
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| classification_rvk | SK 800 SK 830 SK 840 |
| ctrlnum | (OCoLC)6708583 (DE-599)BVBBV003389382 |
| dewey-full | 519.5/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/4 |
| dewey-search | 519.5/4 |
| dewey-sort | 3519.5 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV003389382 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:59:10Z |
| institution | BVB |
| isbn | 0471082678 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002142343 |
| oclc_num | 6708583 |
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| physical | IX, 526 S. |
| psigel | TUB-nveb |
| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| publisher | Wiley |
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| series2 | Wiley series in probability and mathematical statistics |
| spelling | Grenander, Ulf 1923-2016 Verfasser (DE-588)1112557946 aut Abstract inference Ulf Grenander New York [u.a.] Wiley 1981 IX, 526 S. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and mathematical statistics Statistique mathématique Mathematical statistics Statistische Schlussweise (DE-588)4182963-3 gnd rswk-swf Inferenzstatistik (DE-588)4247120-5 gnd rswk-swf Inferenzstatistik (DE-588)4247120-5 s DE-604 Statistische Schlussweise (DE-588)4182963-3 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002142343&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grenander, Ulf 1923-2016 Abstract inference Statistique mathématique Mathematical statistics Statistische Schlussweise (DE-588)4182963-3 gnd Inferenzstatistik (DE-588)4247120-5 gnd |
| subject_GND | (DE-588)4182963-3 (DE-588)4247120-5 |
| title | Abstract inference |
| title_auth | Abstract inference |
| title_exact_search | Abstract inference |
| title_full | Abstract inference Ulf Grenander |
| title_fullStr | Abstract inference Ulf Grenander |
| title_full_unstemmed | Abstract inference Ulf Grenander |
| title_short | Abstract inference |
| title_sort | abstract inference |
| topic | Statistique mathématique Mathematical statistics Statistische Schlussweise (DE-588)4182963-3 gnd Inferenzstatistik (DE-588)4247120-5 gnd |
| topic_facet | Statistique mathématique Mathematical statistics Statistische Schlussweise Inferenzstatistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002142343&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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