Asymptotic expansions for general statistical models:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1985
|
| Series: | Lecture notes in statistics
31 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 505 S. |
| ISBN: | 3540962212 0387962212 |
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MARC
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| 100 | 1 | |a Pfanzagl, Johann |d 1928-2019 |e Verfasser |0 (DE-588)135982200 |4 aut | |
| 245 | 1 | 0 | |a Asymptotic expansions for general statistical models |c J. Pfanzagl |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1985 | |
| 300 | |a VII, 505 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in statistics |v 31 | |
| 650 | 4 | |a Développements asymptotiques | |
| 650 | 4 | |a Statistique mathématique | |
| 650 | 4 | |a Mathematical statistics -- Asymptotic theory | |
| 650 | 4 | |a Asymptotic expansions | |
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Record in the Search Index
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| adam_text |
CONTENTS
0. Introduction 1
O.I. The aim of the book, 1
0.2. About the merits of asymptotic expansions in
statistical theory, 2
0.3. Why a special volume on asymptotic expansions
of second order? 5
0.4. Methodological considerations, 8
0.5. The main results, 1O
O.6. Notations, 14
1. Differentiability of paths 18
1.1. Introduction, 18
1.2. First order differentiability, 20
1.3. First order differentiability with rates, 29
1.4. Some technical lemmas for DCC differentia
b,c
bility, 34
1.5. Local asymptotic normality with rates, 4O
1.6. Second order differentiability of paths, 45
1.7. Second order DCC and Bellinger differentia¬
bility, 52
1.8. Differentiability in b mean, 54
2. Methodological remarks about derivatives and tangent
spaces 57
2.1. Introduction, 57
2.2. Derivatives of derivatives, 62
2.3. Reparametrizations, 65
2.4. Uniqueness of second derivatives, 68
2.5. A product tangent space, 77
IV
3. Examples of derivatives and tangent spaces 86
3.1. Parametric families, 86
3.2. Full families, 92
3.3. Families of symmetric probability measures,
96
3.4. Product measures, 101
4. Differentiability of functional 105
4.1. Basic concepts, 105
4.2. Paths through vector fields, 110
4.3. Second gradients of real valued functionals,
114
4.4. Canonical gradients, 119
4.5. Second gradients for functions of functionals,
124
4.6. Historical remark, 126
5. Examples of functionals and gradients 128
5.1. Parametric families, 128
5.2. Von Mises functionals, 136
5.3. Minimum contrast functionals, 14O
5.4. L functionals, 147
5.5. Quantiles, 149
6. Asymptotic expansions for power functions 153
6.1. Auxiliary results, 153
6.2. The second order envelope power function
for simple hypotheses, 161
6.3. The second order envelope power function
for composite hypotheses, 172
6.4. First order efficient test sequences are
usually second order efficient, 179
6.5. Second order efficiency in one direction
implies second order efficiency in the half
space spanned by this direction over the
hypothesis, 182
6.6. Testing hypotheses on functionals, 193
I
V
7. Evaluating the performance of estimators 198
7.1. Introduction, 198
7.2. Randomized estimators, 199
7.3. Concentration, 202
7.4. Unbiasedness, 205
7.5. Spread, 209
7.6. Comparisons on families of probability
measures, 212
7.7. Multidimensional estimators, 214
7.8. Centering multidimensional probability
measures, 217
7.9. Asymptotic comparisons, 219
7.10. Comparing multidimensional Edgeworth
measures, 227
7.11. comparing one dimensional Edgeworth
measures, 231
7.12. Functions of efficient estimators are
efficient, 235
7.13. Joint efficiency and componentwise effi¬
ciency, 242
8. Asymptotic bounds for the performance of confidence
procedures and estimators 245
8.1. How to measure the quality of a confidence
procedure, 246
8.2. Second order bounds for the concentration
of confidence bounds and median unbiased
estimators, 249
8.3. Second order bounds for the concentration of
confidence bounds and estimators, the distri¬
bution of which admits an asymptotic expan¬
sion, 255
8.4. Interpretation of concentration bounds In
terms of spread, 262
8.5. On local uniformity, 266
8.6. Second order bounds without local uniformity,
272
8.7. First order efficient confidence bounds (and
estimators) are usually second order efficient,
282
VI
9. The possible forms of Edgeworth expansions for
asymptotically efficient estimator sequences 288
9.1. Introduction, 288
9.2. The possible forms of Edgeworth expansions:
The general case, 291
9.3. The possible forms of Edgeworth expansions:
A version without local uniformity, 296
9.4. The possible forms of Edgeworth expansions:
Parametric families, 3OO
9.5. The basic result, 3O4
9.6. Proof of the basic result for p = 1, 306
9.7. Proof of the basic result for arbitrary p,
321
9.8. Examples and counterexamples, 324
9.9. Restriction to subfamilies, 330
10. Statistics with stochastic expansion 333
10.1. Introduction, 333
10.2. Inherent relations for locally uniform
stochastic expansions, 335
10.3. Edgeworth expansions for the distribution of
a statistic admitting a stochastic expansion,
341
10.4. Tests based on test statistics with stochastic
expansion, 347
10.5. Confidence bounds with stochastic expansion,
354
10.6. Estimators with stochastic expansion, 360
10.7. A method for obtaining asymptotically effi¬
cient estimator sequences, 369
10.8. Calibration, 372
10.9. Further remarks on randomized tests and
confidence procedures, 376
11. Examples 382
11.1. Parametric families, 382
11.2. Functionals defined for all probability j
measures, 387 |
11.3. Minimum contrast funotionals, 393 j
VII
11.4. Estimating structural parameters in the
presence of known nuisance parameters, 400
11.5. Estimating structural parameters in the
presence of unknown nuisance parameters, 408
11.6. A special von Mises functional, 419
11.7. Lattice distributions, 425
12. Quantiles: An example of an irregular functional 428
12.1. Introduction, 428
12.2. Bounds for the concentration of confidence
bounds, 429
12.3. Confidence rays for quantiles, 432
12.4. A bound of order o(n ) without local uni¬
formity, 438
12.5. Better confidence bounds without local
uniformity, 441
13. Lemmas 451
13.1. Measurability, 451
13.2. Unimodality, 453
13.3. Probabilistic lemmas, 456
13.4. Moderate deviations and smoothing, 460
13.5. Normal approximation and Edgeworth expan¬
sions, 464
13.6. Order statistics, 477
13.7. Miscellaneous, 48O
References 487
Notation index 498
Author index 500
Subject index 502
List of errata for "Contributions to a General Asymp¬
totic Statistical Theory" 504 |
| any_adam_object | 1 |
| author | Pfanzagl, Johann 1928-2019 |
| author_GND | (DE-588)135982200 |
| author_facet | Pfanzagl, Johann 1928-2019 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| language | English |
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| physical | VII, 505 S. |
| publishDate | 1985 |
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| series | Lecture notes in statistics |
| series2 | Lecture notes in statistics |
| spelling | Pfanzagl, Johann 1928-2019 Verfasser (DE-588)135982200 aut Asymptotic expansions for general statistical models J. Pfanzagl Berlin [u.a.] Springer 1985 VII, 505 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in statistics 31 Développements asymptotiques Statistique mathématique Mathematical statistics -- Asymptotic theory Asymptotic expansions Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Statistisches Modell (DE-588)4121722-6 gnd rswk-swf Statistisches Modell (DE-588)4121722-6 s Asymptotische Entwicklung (DE-588)4112609-9 s DE-604 Lecture notes in statistics 31 (DE-604)BV002447846 31 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000188568&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pfanzagl, Johann 1928-2019 Asymptotic expansions for general statistical models Lecture notes in statistics Développements asymptotiques Statistique mathématique Mathematical statistics -- Asymptotic theory Asymptotic expansions Asymptotische Entwicklung (DE-588)4112609-9 gnd Statistisches Modell (DE-588)4121722-6 gnd |
| subject_GND | (DE-588)4112609-9 (DE-588)4121722-6 |
| title | Asymptotic expansions for general statistical models |
| title_auth | Asymptotic expansions for general statistical models |
| title_exact_search | Asymptotic expansions for general statistical models |
| title_full | Asymptotic expansions for general statistical models J. Pfanzagl |
| title_fullStr | Asymptotic expansions for general statistical models J. Pfanzagl |
| title_full_unstemmed | Asymptotic expansions for general statistical models J. Pfanzagl |
| title_short | Asymptotic expansions for general statistical models |
| title_sort | asymptotic expansions for general statistical models |
| topic | Développements asymptotiques Statistique mathématique Mathematical statistics -- Asymptotic theory Asymptotic expansions Asymptotische Entwicklung (DE-588)4112609-9 gnd Statistisches Modell (DE-588)4121722-6 gnd |
| topic_facet | Développements asymptotiques Statistique mathématique Mathematical statistics -- Asymptotic theory Asymptotic expansions Asymptotische Entwicklung Statistisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000188568&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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