Normal approximation: new results, methods and problems
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Utrecht
VSP
1998
|
| Edition: | 1. publ. |
| Series: | Modern probabilty and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 363 S. |
| ISBN: | 9067642924 9789067642927 |
Staff View
MARC
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| 100 | 1 | |a Senatov, Vladimir V. |e Verfasser |0 (DE-588)143069934 |4 aut | |
| 245 | 1 | 0 | |a Normal approximation |b new results, methods and problems |c Vladimir V. Senatov |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Utrecht |b VSP |c 1998 | |
| 300 | |a VII, 363 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Modern probabilty and statistics | |
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| 650 | 7 | |a Probabilités |2 ram | |
| 650 | 7 | |a Transformations (mathématiques) |2 ram | |
| 650 | 7 | |a métrique |2 inriac | |
| 650 | 7 | |a probabilité |2 inriac | |
| 650 | 7 | |a statistique |2 inriac | |
| 650 | 4 | |a Approximation theory | |
| 650 | 4 | |a Probabilities | |
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Record in the Search Index
| _version_ | 1804127307717148672 |
|---|---|
| adam_text | Contents
Foreword
iii
Preface v
1
Introduction
1
1.1
Formulation of the problem
...................... 1
1.2
Historical aspects; Qualitative effects of transition from the one-
dimensional case to multidimensional spaces
........... 3
1.3
On the contents of the book
...................... 32
1.4
Some notation and definitions
.................... 34
2
Elements of the theory of probability metrics
39
2.1
Basic probability metrics
....................... 40
2.2
On distinctions between probability metrics
............ 45
2.3
Special properties of probability metrics
.............. 47
2.4
Relations between metrics
...................... 52
2.5
Structure of the set of metrics
.................... 53
2.6
Estimates in equivalent metrics
................... 61
2.7
The
Lévy-Prokhorov
metrics; Weak convergence
......... 62
2.8
Uniform metrics
............................ 83
2.9
Metrics
Я
and#
............................ 89
2.10
Ideal metrics
.............................. 99
2.11
Extremal properties of
L
and
ρ
metrics
............... 124
3
Method of characteristic functions; Berry-Esseen theorem
129
3.1
Basic properties of characteristic functions
............. 130
3.2
Estimation of closeness of characteristic functions in CLT
.... 132
3.3
Berry-Esseen inequality
....................... 136
3.4
Berry-Esseen theorem
........................ 139
3.5
Modifications of Berry-Esseen theorem
............... 140
3.6
One remark about the method of characteristic functions in the
multidimensional case
........................ 151
4
Method of
compositions
in the one-dimensional case
153
4.1
Preliminary remarks
......................... 154
4.2
Smoothing inequality
......................... 159
4.3
Basic estimate
............................. 162
4.4
Speculations
.............................. 165
4.5
One modification of the method of compositions
.......... 167
4.6
Convergence rate estimate under the condition fa+s
<
oo,
0 <
б
< 1 ................................ 175
5
Method of compositions in the multidimensional case
179
5.1
Base estimates
.............................180
5.2
Estimates under the condition
Var(P„,O)
-> 0...........185
6
Convergence rate estimates in weak metrics
193
6.1
On a relation between estimates of the
Lévy-Prokhorov
metrics
193
6.2
Estimation of the metrics
π
through the metrics
ζ
........ 196
6.3
Estimation of
π(Ρη, Φ;
6)
in the space l2
.............. 203
6.4
Estimation of
π(Ρη,Φ;©)
and
π(Ρη,Φ;
95)
in the space.E*
..... 206
6.5
Estimation of
π(Ρη,Φ;
05)
in the space £2
.............. 210
6.6
A remark on the estimates in the central limit theorem for weak
metrics
................................. 215
7
Estimation of uniform distances in £2
217
7.1
Some remarks on the method to prove the estimates
.......218
7.2
Additional notation
..........................230
7.3
Formulation and proof of the theorem
................232
8
Estimation of derivatives and measures
277
8.1
Derivatives of the functions
ξ(τ^χ)
—
p)lp) and
цігфо
—
p)lp)
. . 211
8.2
Derivatives of the normal law
....................281
8.3
Estimates of the Pn-measure of the sets F(e) and
Φ(ε)
......304
8.4
On a bound in the space Ek
......................331
9
Lower bounds for uniform metrics
337
Conclusion
351
Bibliography
355
Index
363
|
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| author | Senatov, Vladimir V. |
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| author_facet | Senatov, Vladimir V. |
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| classification_rvk | SK 800 |
| ctrlnum | (OCoLC)41221991 (DE-599)BVBBV012650749 |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV012650749 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:31:16Z |
| institution | BVB |
| isbn | 9067642924 9789067642927 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008594967 |
| oclc_num | 41221991 |
| open_access_boolean | |
| owner | DE-739 |
| owner_facet | DE-739 |
| physical | VII, 363 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | VSP |
| record_format | marc |
| series2 | Modern probabilty and statistics |
| spelling | Senatov, Vladimir V. Verfasser (DE-588)143069934 aut Normal approximation new results, methods and problems Vladimir V. Senatov 1. publ. Utrecht VSP 1998 VII, 363 S. txt rdacontent n rdamedia nc rdacarrier Modern probabilty and statistics Fonctions (mathématiques) ram Gauss, Loi de (statistique) ram Poisson, Distribution de ram Probabilités ram Transformations (mathématiques) ram métrique inriac probabilité inriac statistique inriac Approximation theory Probabilities Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008594967&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Senatov, Vladimir V. Normal approximation new results, methods and problems Fonctions (mathématiques) ram Gauss, Loi de (statistique) ram Poisson, Distribution de ram Probabilités ram Transformations (mathématiques) ram métrique inriac probabilité inriac statistique inriac Approximation theory Probabilities |
| title | Normal approximation new results, methods and problems |
| title_auth | Normal approximation new results, methods and problems |
| title_exact_search | Normal approximation new results, methods and problems |
| title_full | Normal approximation new results, methods and problems Vladimir V. Senatov |
| title_fullStr | Normal approximation new results, methods and problems Vladimir V. Senatov |
| title_full_unstemmed | Normal approximation new results, methods and problems Vladimir V. Senatov |
| title_short | Normal approximation |
| title_sort | normal approximation new results methods and problems |
| title_sub | new results, methods and problems |
| topic | Fonctions (mathématiques) ram Gauss, Loi de (statistique) ram Poisson, Distribution de ram Probabilités ram Transformations (mathématiques) ram métrique inriac probabilité inriac statistique inriac Approximation theory Probabilities |
| topic_facet | Fonctions (mathématiques) Gauss, Loi de (statistique) Poisson, Distribution de Probabilités Transformations (mathématiques) métrique probabilité statistique Approximation theory Probabilities |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008594967&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT senatovvladimirv normalapproximationnewresultsmethodsandproblems |