Robust and non-robust models in statistics:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Nova Science Publ.
2009
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVI, 317 S. |
| ISBN: | 9781607417682 |
Internformat
MARC
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| 008 | 091105s2009 xxu |||| 00||| eng d | ||
| 010 | |a 2009017712 | ||
| 020 | |a 9781607417682 |c hardcover |9 978-1-607-41768-2 | ||
| 035 | |a (OCoLC)320352402 | ||
| 035 | |a (DE-599)BVBBV035809500 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
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| 100 | 1 | |a Klebanov, Lev B. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Robust and non-robust models in statistics |c Lev B. Klebanov, Svetlozar T. Rachev, and Frank J. Fabozzi |
| 264 | 1 | |a New York |b Nova Science Publ. |c 2009 | |
| 300 | |a XVI, 317 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Limit theorems (Probability theory) | |
| 650 | 4 | |a Estimation theory | |
| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 4 | |a Robust statistics | |
| 650 | 4 | |a Random variables | |
| 650 | 0 | 7 | |a Robuste Statistik |0 (DE-588)4451047-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Grenzwertsatz |0 (DE-588)4158163-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Inkorrekt gestelltes Problem |0 (DE-588)4186951-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Inkorrekt gestelltes Problem |0 (DE-588)4186951-5 |D s |
| 689 | 0 | 1 | |a Grenzwertsatz |0 (DE-588)4158163-5 |D s |
| 689 | 0 | 2 | |a Robuste Statistik |0 (DE-588)4451047-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Račev, Svetlozar T. |d 1951- |e Verfasser |0 (DE-588)12022979X |4 aut | |
| 700 | 1 | |a Fabozzi, Frank J. |d 1948- |e Verfasser |0 (DE-588)129772054 |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018668449&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018668449 | ||
Datensatz im Suchindex
| _version_ | 1804140760109416448 |
|---|---|
| adam_text | Contents
Preface
xj¡¡
I Models in Statistical Estimation Theory
3
1
111-Posed Problems
5
1.1
Introduction and Motivating Examples
................. 5
1.1.1
Two Motivating examples
.................... 5
1.1.2
Principal idea
........................... 8
1.2
Central Pre-Limit Theorem
....................... 10
1.3
Sums of a Random Number of Random Variables
........... 13
1.4
Local Pre-Limit Theorems and Their Applications to Finance
.... 14
1.5
Pre-Limit Theorem for Extremums
.................. 15
1.6
Relations with Robustness of Statistical Estimators
.......... 17
1.7
Statistical Estimation for Non-Smooth Densities
........... 20
1.8
Key points of this chapter
........................ 27
2
Loss Functions and the Restrictions Imposed on the Model
29
2.1
Introduction
................................ 29
2.2
Reducible Families of Functions
..................... 30
2.2.1
Weakly reducible families
.................... 31
2.2.2
Reducible families
........................ 34
2.2.3
Strongly reducible families
.................... 36
2.2.4
Reducible and non-reducible families
.............. 37
2.3
The Classification of Classes of Estimators by Their Completeness
Types
................................... 38
2.3.1
Completeness properties
..................... 38
2.3.2
Loss functions satisfying the four conditions
.......... 41
2.4
An Example of a Loss Function
..................... 49
2.4.1
A class of loss functions
..................... 50
2.5
Concluding Remarks
...........................
5**
2.6
Key points of this chapter
........................
54
ix
_______
Lev
В.
Klebanov, Svetlozar
T.
Rachev, and Frank J. Fabozzi
__________
Loss Functions and the Theory of Unbiased Estimation
57
3.1
Introduction
................................ 57
3.2
Unbiasedness, Lehmann s Unbiasedness, and Wi-Unbiasedness
... 57
3.3
Characterizations of Convex and Strictly Convex Loss Functions
. . 60
3.3.1
Regular unbiasedness
...................... 61
3.4
Unbiased Estimation, Universal Loss Functions, and Optimal Subal-
gebras
................................... 71
3.4.1
Unbiased estimators
....................... 72
3.4.2
i^i-unbiased estimators
..................... 75
3.5
Matrix-Valued Loss Functions
...................... 89
3.6
Concluding Remarks
........................... 91
3.7
Key points of this chapter
........................ 92
Sufficient Statistics
95
4.1
Introduction
................................ 95
4.2
Completeness and Sufficiency
...................... 95
4.3
Sufficiency When Nuisance Parameters are Present
.......... 100
4.4
Bayes
Estimators Independent of the Loss Function
.......... 107
4.5
Key points of this chapter
........................ 114
Parametric Inference
115
5.1
Introduction
................................ 115
5.2
Parametric Density Estimation versus Parameter Estimation
.... 115
5.2.1
Some definitions
......................... 116
5.3
Unbiased Parametric Inference
..................... 117
5.3.1
Unbiased estimators of parametric functions and of the density
119
5.3.2
Estimating the characteristic and distribution functions
. . . 123
5.4
Bayesian Parametric Inference
...................... 124
5.5
Parametric Density Estimation for Location Families
......... 127
5.5.1
The problem of the complexity of estimators
......... 129
5.6
Key points of this chapter
........................ 132
Trimmed,
Bayes,
and Admissible Estimators
133
6.1
Introduction
................................ 133
6.2
A trimmed Estimator cannot be Bayesian
............... 133
6.3
Linear Regression Model: Trimmed Estimators and Admissibility
. . 135
6.4
Key points of this chapter
........................ 138
Characterization of Distributions and Intensively Monotone Oper¬
ators
139
7.1
Introduction
................................
I39
7.2
The Uniqueness of Solutions of Operator Equations
.......... 140
7.3
Examples of Intensively Monotone Operators
............. 145
Contents
7.4
Examples of Strongly ¿-Positive Families
............... 148
7.5
A Generalization of Cramer s and
Pòlya s
Theorems
......... 153
7.6
Random Linear Forms
........................
15g
7.7
Some Problems Related to Reliability Theory
............. 161
7.7.1
Relations of reliabilities of two systems
............. 161
7.7.2
Characterization by relevation-type equality
.......... 165
7.7.3
Recovering a distribution of failures by the reliabilities of sys¬
tems
................................ 168
7.8
Key points of this chapter
........................ 170
II Robustness for a Fixed Number of Observations
171
8
Robustness of Statistical Models
173
8.1
Introduction
................................ 173
8.2
Preliminaries
............................... 173
8.3
Robustness in Statistical Estimation and the Loss Function
..... 175
8.4
A Linear Method of Statistical Estimation
............... 185
8.5
Polynomial and Modified Polynomial Pitman Estimators
....... 194
8.6
Non-Admissibility of Polynomial Estimators of Location
....... 200
8.7
The Asymptotic
ε
-Admisibility
of the Polynomial Pitman s Estima¬
tors of the Location Parameter
..................... 208
8.7.1
Asymptotic
ε
-admissibility
of a linear estimator
........ 208
8.7.2
Asymptotic
ε
-admissibility
of a polynomila Pitman estimator
213
8.8
Key points of this chapter
........................ 217
9
Entire Function of Finite Exponential Type and Estimation of Den¬
sity Function
219
9.1
Introduction
................................
219
9.2
Main Definitions
............................. 219
9.3
Fourier Transform of the Functions from WlVJ)
............. 223
9.4
Interpolation Formula
.......................... 225
9.5
Inequality of Different Metrics
...................... 226
9.6
Valle e
Poussin
Kernels
..........................
226
9.7
Key points of this chapter
........................
234
Ш
Metric Methods in Statistics 235
10
St-Metrics in the Set of Probability Measures
237
10.1
Introduction
................................
237
10.2
A Class of Positive Definite Kernels in the Set of Probabilities and
^t-Distances
................................
xii_______
Lev
В.
Klebanov, Svetlozar
T.
Rachev, and Frank J. Fabozzi
__________
10.3
m-Negative Definite Kernels and Metrics
................ 241
10.4
Statistical Estimates Obtained by the Minimal Distances Method
. . 245
10.4.1
Estimating a location parameter, I
............... 245
10.4.2
Estimating a location parameter, II
.............. 248
10.4.3
Estimating a general parameter
................. 249
10.4.4
Estimating a location parameter, III
.............. 251
10.4.5
Semiparametric estimation
................... 252
10.5
Key points of this chapter
........................ 253
11
Some Statistical Tests Based on W-Distances
255
11.1
Introduction
................................ 255
11.2
Multivariate Two-Sample Test
..................... 255
11.3
Test for Two Distributions to Belong to the Same Additive Type
. . 258
11.4
Some Tests for Observations to be Gaussian
.............. 260
11.5
A Test for Closeness of Probability Distributions
........... 262
11.6
Key points of this chapter
........................ 264
A Generalized Functions
265
A.I Main definitions
............................. 265
A.2 Definition of Fourier Transform for Generalized Functions
...... 270
A.3 Functions
ψε
and
ψε
........................... 274
В
Positive and Negative Definite Kernels and Their Properties
277
B.I Definitions of Positive and Negative Definite Kernels
......... 277
B.2 Examples of Positive Definite Kernels
................. 281
B.3 Positive Definite Functions
....................... 284
B.4 Negative Definite Kernels
........................ 285
B.5 Coarse Embeddings of Metric Spaces into Hubert Space
....... 289
B.6 Strictly and Strongly Positive and Negative Definite Kernels
..... 290
Bibliography
295
Authors Index
313
Index
315
|
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| author | Klebanov, Lev B. Račev, Svetlozar T. 1951- Fabozzi, Frank J. 1948- |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| institution | BVB |
| isbn | 9781607417682 |
| language | English |
| lccn | 2009017712 |
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| spelling | Klebanov, Lev B. Verfasser aut Robust and non-robust models in statistics Lev B. Klebanov, Svetlozar T. Rachev, and Frank J. Fabozzi New York Nova Science Publ. 2009 XVI, 317 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Limit theorems (Probability theory) Estimation theory Distribution (Probability theory) Robust statistics Random variables Robuste Statistik (DE-588)4451047-0 gnd rswk-swf Grenzwertsatz (DE-588)4158163-5 gnd rswk-swf Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd rswk-swf Inkorrekt gestelltes Problem (DE-588)4186951-5 s Grenzwertsatz (DE-588)4158163-5 s Robuste Statistik (DE-588)4451047-0 s DE-604 Račev, Svetlozar T. 1951- Verfasser (DE-588)12022979X aut Fabozzi, Frank J. 1948- Verfasser (DE-588)129772054 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018668449&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Klebanov, Lev B. Račev, Svetlozar T. 1951- Fabozzi, Frank J. 1948- Robust and non-robust models in statistics Limit theorems (Probability theory) Estimation theory Distribution (Probability theory) Robust statistics Random variables Robuste Statistik (DE-588)4451047-0 gnd Grenzwertsatz (DE-588)4158163-5 gnd Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd |
| subject_GND | (DE-588)4451047-0 (DE-588)4158163-5 (DE-588)4186951-5 |
| title | Robust and non-robust models in statistics |
| title_auth | Robust and non-robust models in statistics |
| title_exact_search | Robust and non-robust models in statistics |
| title_full | Robust and non-robust models in statistics Lev B. Klebanov, Svetlozar T. Rachev, and Frank J. Fabozzi |
| title_fullStr | Robust and non-robust models in statistics Lev B. Klebanov, Svetlozar T. Rachev, and Frank J. Fabozzi |
| title_full_unstemmed | Robust and non-robust models in statistics Lev B. Klebanov, Svetlozar T. Rachev, and Frank J. Fabozzi |
| title_short | Robust and non-robust models in statistics |
| title_sort | robust and non robust models in statistics |
| topic | Limit theorems (Probability theory) Estimation theory Distribution (Probability theory) Robust statistics Random variables Robuste Statistik (DE-588)4451047-0 gnd Grenzwertsatz (DE-588)4158163-5 gnd Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd |
| topic_facet | Limit theorems (Probability theory) Estimation theory Distribution (Probability theory) Robust statistics Random variables Robuste Statistik Grenzwertsatz Inkorrekt gestelltes Problem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018668449&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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