Theory of statistics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
1995
|
| Series: | Springer series in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 675 - 688 |
| Physical Description: | XVI, 702 S. Illustrationen |
| ISBN: | 0387945466 |
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MARC
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| 100 | 1 | |a Schervish, Mark J. |e Verfasser |0 (DE-588)171047923 |4 aut | |
| 245 | 1 | 0 | |a Theory of statistics |c Mark J. Schervish |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1995 | |
| 300 | |a XVI, 702 S. |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer series in statistics | |
| 500 | |a Literaturverz. S. 675 - 688 | ||
| 650 | 7 | |a Mathematical statistics |2 sbt | |
| 650 | 4 | |a Mathematical statistics | |
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Record in the Search Index
| _version_ | 1807773903998681088 |
|---|---|
| adam_text |
CONTENTS
PREFACE
V
IJ
CHAPTER
1:
PROBABILITY
MODELS
1
1.1
BACKGROUND
.
1
1.1.1
GENERAL
CONCEPTS
.
1
1.1.2
CLASSICAL
STATISTICS
.
2
1.1.3
BAYESIAN
STATISTICS
.
4
1.2
EXCHANGEABILITY
.
5
1.2.1
DISTRIBUTIONAL
SYMMETRY
.
5
1.2.2
FREQUENCY
AND
EXCHANGEABILITY
.
10
1.3
PARAMETRIC
MODELS
.
12
1.3.1
PRIOR,
POSTERIOR,
AND
PREDICTIVE
DISTRIBUTIONS
.
13
1.3.2
IMPROPER
PRIOR
DISTRIBUTIONS
.
.
19
1.3.3
CHOOSING
PROBABILITY
DISTRIBUTIONS
.
21
1.4
DEFINETTI
'
S
REPRESENTATION
THEOREM
.
24
1.4.1
UNDERSTANDING
THE
THEOREMS
.
24
1.4.2
THE
MATHEMATICAL
STATEMENTS
.
26
1.4.3
SOME
EXAMPLES
.
28
1.5
PROOFS
OF
DEFINETTI
'
S
THEOREM
AND
RELATED
RESULTS*
.
33
1.5.1
STRONG
LAW
OF
LARGE
NUMBERS
.
33
1.5.2
THE
BERNOULLI
CASE
.
36
1.5.3
THE
GENERAL
FINITE
CASE*
.
38
1.5.4
THE
GENERAL
INFINITE
CASE
.
45
1.5.5
FORMAL
INTRODUCTION
TO
PARAMETRIC
MODELS*
.
49
1.6
INFINITE-DIMENSIONAL
PARAMETERS*
.
52
1.6.1
DIRICHLET
PROCESSES
.
52
1.6.2
TAILFREE
PROCESSES
+
.
60
1.7
PROBLEMS
.
73
CHAPTER
2:
SUFFICIENT
STATISTICS
82
2.1
DEFINITIONS
.
82
2.1.1
NOTATIONAL
OVERVIEW
.
82
2.1.2
SUFFICIENCY
.
83
2.1.3
MINIMAL
AND
COMPLETE
SUFFICIENCY
.
92
2.1.4
ANCILLARITY
.
95
2.2
EXPONENTIAL
FAMILIES
OF
DISTRIBUTIONS
.
102
XII
CONTENTS
2.2.1
BASIC
PROPERTIES
.
102
2.2.2
SMOOTHNESS
PROPERTIES
.
105
2.2.3
A
CHARACTERIZATION
THEOREM*
.
109
2.3
INFORMATION
.
110
2.3.1
FISHER
INFORMATION
.
ILL
2.3.2
KULLBACK-LEIBLER
INFORMATION
.
115
2.3.3
CONDITIONAL
INFORMATION*
.
118
2.3.4
JEFFREYS
'
PRIOR*
.
121
2.4
EXTREMAL
FAMILIES*
.
123
2.4.1
THE
MAIN
RESULTS
.
124
2.4.2
EXAMPLES
.
127
2.4.3
PROOFS
+
.
129
2.5
PROBLEMS
.
138
CHAPTER
3:
DECISION
THEORY
144
3.1
DECISION
PROBLEMS
.
144
3.1.1
FRAMEWORK
.
144
3.1.2
ELEMENTS
OF
BAYESIAN
DECISION
THEORY
.
146
3.1.3
ELEMENTS
OF
CLASSICAL
DECISION
THEORY
.
149
3.1.4
SUMMARY
.
150
3.2
CLASSICAL
DECISION
THEORY
.
150
3.2.1
THE
ROLE
OF
SUFFICIENT
STATISTICS
.
150
3.2.2
ADMISSIBILITY
.
153
3.2.3
JAMES-STEIN
ESTIMATORS
.
163
3.2.4
MINIMAX
RULES
.
167
3.2.5
COMPLETE
CLASSES
.
174
3.3
AXIOMATIC
DERIVATION
OF
DECISION
THEORY*
.
181
3.3.1
DEFINITIONS
AND
AXIOMS
.
181
3.3.2
EXAMPLES
.
186
3.3.3
THE
MAIN
THEOREMS
.
188
3.3.4
RELATION
TO
DECISION
THEORY
.
189
3.3.5
PROOFS
OF
THE
MAIN
THEOREMS*
.
190
3.3.6
STATE-DEPENDENT
UTILITY*
.
205
3.4
PROBLEMS
.
208
CHAPTER
4:
HYPOTHESIS
TESTING
214
4.1
INTRODUCTION
.
214
4.1.1
A
SPECIAL
KIND
OF
DECISION
PROBLEM
.
214
4.1.2
PURE
SIGNIFICANCE
TESTS
.
216
4.2
BAYESIAN
SOLUTIONS
.
218
4.2.1
TESTING
IN
GENERAL
.
218
4.2.2
BAYES
FACTORS
.
220
4.3
MOST
POWERFUL
TESTS
.
230
4.3.1
SIMPLE
HYPOTHESES
AND
ALTERNATIVES
.
233
4.3.2
SIMPLE
HYPOTHESES,
COMPOSITE
ALTERNATIVES
.
238
4.3.3
ONE-SIDED
TESTS
.
239
4.3.4
TWO-SIDED
HYPOTHESES
.
246
4.4
UNBIASED
TESTS
.
253
4.4.1
GENERAL
RESULTS
.
253
CONTENTS
XIII
4.4,2
INTERVAL
HYPOTHESES
.
255
4.4.3
POINT
HYPOTHESES
.
257
4.5
NUISANCE
PARAMETERS
.
265
4.5.1
NEYMAN
STRUCTURE
.
265
4.5.2
TESTS
ABOUT
NATURAL
PARAMETERS
.
268
4.5.3
LINEAR
COMBINATIONS
OF
NATURAL
PARAMETERS
.
272
4.5.4
OTHER
TWO-SIDED
CASES*
.
272
4.5.5
LIKELIHOOD
RATIO
TESTS
.
274
4.5.6
THE
STANDARD
F-TEST
AS
A
BAYES
RULE*
.
276
4.6
P
VALUES
.
279
4.6.1
DEFINITIONS
AND
EXAMPLES
.
279
4.6.2
P-VALUES
AND
BAYES
FACTORS
.
283
4.7
PROBLEMS
.
285
CHAPTER
5:
ESTIMATION
296
5.1
POINT
ESTIMATION
.
296
5.1.1
MINIMUM
VARIANCE
UNBIASED
ESTIMATION
.
297
5.1.2
LOWER
BOUNDS
ON
THE
VARIANCE
OF
UNBIASED
ESTIMATORS
.
.
.
301
5.1.3
MAXIMUM
LIKELIHOOD
ESTIMATION
.
307
5.1.4
BAYESIAN
ESTIMATION
.
309
5.1.5
ROBUST
ESTIMATION*
.
310
5.2
SET
ESTIMATION
.
315
5.2.1
CONFIDENCE
SETS
.
315
5.2.2
PREDICTION
SETS*
.
324
5.2.3
TOLERANCE
SETS*
.
325
5.2.4
BAYESIAN
SET
ESTIMATION
.
327
5.2.5
DECISION
THEORETIC
SET
ESTIMATION*
.
328
5.3
THE
BOOTSTRAP*
.
329
5.3.1
THE
GENERAL
CONCEPT
.
329
5.3.2
STANDARD
DEVIATIONS
AND
BIAS
.
335
5.3.3
BOOTSTRAP
CONFIDENCE
INTERVALS
.
336
5.4
PROBLEMS
.
339
CHAPTER
6:
EQUIVARIANCE*
344
6.1
COMMON
EXAMPLES
.
344
6.1.1
LOCATION
PROBLEMS
.
344
6.1.2
SCALE
PROBLEMS*
.
350
6.2
EQUIVARIANT
DECISION
THEORY
.
353
6.2.1
GROUPS
OF
TRANSFORMATIONS
.
353
6.2.2
EQUIVARIANCE
AND
CHANGES
OF
UNITS
.
359
6.2.3
MINIMUM
RISK
EQUIVARIANT
DECISIONS
.
363
6.3
TESTING
AND
CONFIDENCE
INTERVALS*
.
375
6.3.1
P-VALUES
IN
INVARIANT
PROBLEMS
.
375
6.3.2
EQUIVARIANT
CONFIDENCE
SETS
.
379
6.3.3
INVARIANT
TESTS*
.
380
6.4
PROBLEMS
.
388
XIV
CONTENTS
CHAPTER
7:
LARGE
SAMPLE
THEORY
394
7.1
CONVERGENCE
CONCEPTS
.
394
7.1.1
DETERMINISTIC
CONVERGENCE
.
394
7.1.2
STOCHASTIC
CONVERGENCE
.
395
7.1.3
THE
DELTA
METHOD
.
401
7.2
SAMPLE
QUANTILES
.
404
7.2.1
A
SINGLE
QUANTILE
.
404
7.2.2
SEVERAL
QUANTILES
.
408
7.2.3
LINEAR
COMBINATIONS
OF
QUANTILES*
.
410
7.3
LARGE
SAMPLE
ESTIMATION
.
412
7.3.1
SOME
PRINCIPLES
OF
LARGE
SAMPLE
ESTIMATION
.
412
7.3.2
MAXIMUM
LIKELIHOOD
ESTIMATORS
.
415
7.3.3
MLES
IN
EXPONENTIAL
FAMILIES
.
418
7.3.4
EXAMPLES
OF
INCONSISTENT
MLES
.
420
7.3.5
ASYMPTOTIC
NORMALITY
OF
MLES
.
421
7.3.6
ASYMPTOTIC
PROPERTIES
OF
M-ESTIMATORS*
.
424
7.4
LARGE
SAMPLE
PROPERTIES
OF
POSTERIOR
DISTRIBUTIONS
.
428
7.4.1
CONSISTENCY
OF
POSTERIOR
DISTRIBUTIONS
+
.
429
7.4.2
ASYMPTOTIC
NORMALITY
OF
POSTERIOR
DISTRIBUTIONS
.
435
7.4.3
LAPLACE
APPROXIMATIONS
TO
POSTERIOR
DISTRIBUTIONS*
.
446
7.4.4
ASYMPTOTIC
AGREEMENT
OF
PREDICTIVE
DISTRIBUTIONS"
1
"
.
455
7.5
LARGE
SAMPLE
TESTS
.
458
7.5.1
LIKELIHOOD
RATIO
TESTS
.
458
7.5.2
CHI-SQUARED
GOODNESS
OF
FIT
TESTS
.
461
7.6
PROBLEMS
.
467
CHAPTER
8:
HIERARCHICAL
MODELS
476
8.1
INTRODUCTION
.
476
8.1.1
GENERAL
HIERARCHICAL
MODELS
.
476
8.1.2
PARTIAL
EXCHANGEABILITY*
.
479
8.1.3
EXAMPLES
OF
THE
REPRESENTATION
THEOREM*
.
480
8.2
NORMAL
LINEAR
MODELS
.
483
8.2.1
ONE-WAY
ANOVA
.
483
8.2.2
TWO-WAY
MIXED
MODEL
ANOVA*
.
488
8.2.3
HYPOTHESIS
TESTING
.
491
8.3
NONNORMAL
MODELS*
.
495
8.3.1
POISSON
PROCESS
DATA
.
495
8.3.2
BERNOULLI
PROCESS
DATA
.
497
8.4
EMPIRICAL
BAYES
ANALYSIS*
.
500
8.4.1
NAIVE
EMPIRICAL
BAYES
.
500
8.4.2
ADJUSTED
EMPIRICAL
BAYES
.
503
8.4.3
UNEQUAL
VARIANCE
CASE
.
504
8.5
SUCCESSIVE
SUBSTITUTION
SAMPLING
.
505
8.5.1
THE
GENERAL
ALGORITHM
.
505
8.5.2
NORMAL
HIERARCHICAL
MODELS
.
512
8.5.3
NONNORMAL
MODELS
.
517
8.6
MIXTURES
OF
MODELS
.
519
8.6.1
GENERAL
MIXTURE
MODELS
.
519
8.6.2
OUTLIERS
.
521
CONTENTS
XV
8.6.3
BAYESIAN
ROBUSTNESS
.
524
8.7
PROBLEMS
.
532
CHAPTER
9:
SEQUENTIAL
ANALYSIS
536
9.1
SEQUENTIAL
DECISION
PROBLEMS
.
536
9.2
THE
SEQUENTIAL
PROBABILITY
RATIO
TEST
.
548
9.3
INTERVAL
ESTIMATION*
.
558
9.4
THE
RELEVANCE
OF
STOPPING
RULES
.
562
9.5
PROBLEMS
.
567
APPENDIX
A:
MEASURE
AND
INTEGRATION
THEORY
570
A.L
OVERVIEW
.
570
A.
1.1
DEFINITIONS
.
570
A.
1.2
MEASURABLE
FUNCTIONS
.
572
A.
1.3
INTEGRATION
.
573
A.
1.4
ABSOLUTE
CONTINUITY
.
574
A.
2
MEASURES
.
575
A.
3
MEASURABLE
FUNCTIONS
.
582
A.4
INTEGRATION
.
587
A.
5
PRODUCT
SPACES
.
593
A.6
ABSOLUTE
CONTINUITY
.
597
A.
7
PROBLEMS
.
602
APPENDIX
B:
PROBABILITY
THEORY
606
B.L
OVERVIEW
.
606
B.L.L
MATHEMATICAL
PROBABILITY
.
606
B.L.
2
CONDITIONING
.
607
B.L.
3
LIMIT
THEOREMS
.
611
B.2
MATHEMATICAL
PROBABILITY
.
612
B.2.1
RANDOM
QUANTITIES
AND
DISTRIBUTIONS
.
612
B.2.
2
SOME
USEFUL
INEQUALITIES
.
613
B.3
CONDITIONING
.
615
B.3.1
CONDITIONAL
EXPECTATIONS
.
615
B.3.2
BOREL
SPACES*
.
619
B.3.
3
CONDITIONAL
DENSITIES
.
623
B.3.4
CONDITIONAL
INDEPENDENCE
.
628
B.3.5
THE
LAW
OF
TOTAL
PROBABILITY
.
632
B.4
LIMIT
THEOREMS
.
634
B.4.1
CONVERGENCE
IN
DISTRIBUTION
AND
IN
PROBABILITY
.
634
B.4.2
CHARACTERISTIC
FUNCTIONS
.
639
B.5
STOCHASTIC
PROCESSES
.
645
B.5.1
INTRODUCTION
.
645
B.5.
2
MARTINGALES
4
.
645
B.5.
3
MARKOV
CHAINS*
.
650
B.5.4
GENERAL
STOCHASTIC
PROCESSES
.
651
B.6
SUBJECTIVE
PROBABILITY
.
654
B.7
SIMULATION*
.
659
B.8
PROBLEMS
.
661
XVI
CONTENTS
APPENDIX
C:
MATHEMATICAL
THEOREMS
NOT
PROVEN
HERE
665
C.L
REAL
ANALYSIS
.
665
C.2
COMPLEX
ANALYSIS
.
666
C.3
FUNCTIONAL
ANALYSIS
.
667
APPENDIX
D:
SUMMARY
OF
DISTRIBUTIONS
668
D.L
UNIVARIATE
CONTINUOUS
DISTRIBUTIONS
.
668
D.2
UNIVARIATE
DISCRETE
DISTRIBUTIONS
.
672
D.3
MULTIVARIATE
DISTRIBUTIONS
.
674
REFERENCES
675
NOTATION
AND
ABBREVIATION
INDEX
689
NAME
INDEX
691
SUBJECT
INDEX
694 |
| any_adam_object | 1 |
| author | Schervish, Mark J. |
| author_GND | (DE-588)171047923 |
| author_facet | Schervish, Mark J. |
| author_role | aut |
| author_sort | Schervish, Mark J. |
| author_variant | m j s mj mjs |
| building | Verbundindex |
| bvnumber | BV010445651 |
| callnumber-first | Q - Science |
| callnumber-label | QA276 |
| callnumber-raw | QA276.S346 1995 |
| callnumber-search | QA276.S346 1995 |
| callnumber-sort | QA 3276 S346 41995 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 231 SK 830 SK 840 |
| classification_tum | MAT 620f |
| ctrlnum | (OCoLC)246760891 (DE-599)BVBBV010445651 |
| dewey-full | 519.5 519.520 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 519.5 20 |
| dewey-search | 519.5 519.5 20 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV010445651 |
| illustrated | Illustrated |
| indexdate | 2024-08-19T00:32:20Z |
| institution | BVB |
| isbn | 0387945466 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006961950 |
| oclc_num | 246760891 |
| open_access_boolean | |
| owner | DE-29T DE-N2 DE-19 DE-BY-UBM DE-703 DE-12 DE-739 DE-824 DE-384 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-20 DE-521 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-29T DE-N2 DE-19 DE-BY-UBM DE-703 DE-12 DE-739 DE-824 DE-384 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-20 DE-521 DE-634 DE-83 DE-11 DE-188 |
| physical | XVI, 702 S. Illustrationen |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spelling | Schervish, Mark J. Verfasser (DE-588)171047923 aut Theory of statistics Mark J. Schervish New York [u.a.] Springer 1995 XVI, 702 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Literaturverz. S. 675 - 688 Mathematical statistics sbt Mathematical statistics Schätztheorie (DE-588)4121608-8 gnd rswk-swf Auswahlfunktion (DE-588)4134349-9 gnd rswk-swf Statistischer Test (DE-588)4077852-6 gnd rswk-swf Entscheidungstheorie (DE-588)4138606-1 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Varianzanalyse (DE-588)4187413-4 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Statistik (DE-588)4056995-0 s DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s 1\p DE-604 Entscheidungstheorie (DE-588)4138606-1 s 2\p DE-604 Schätztheorie (DE-588)4121608-8 s 3\p DE-604 Varianzanalyse (DE-588)4187413-4 s 4\p DE-604 Statistischer Test (DE-588)4077852-6 s 5\p DE-604 Auswahlfunktion (DE-588)4134349-9 s 6\p DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006961950&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Schervish, Mark J. Theory of statistics Mathematical statistics sbt Mathematical statistics Schätztheorie (DE-588)4121608-8 gnd Auswahlfunktion (DE-588)4134349-9 gnd Statistischer Test (DE-588)4077852-6 gnd Entscheidungstheorie (DE-588)4138606-1 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Varianzanalyse (DE-588)4187413-4 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4121608-8 (DE-588)4134349-9 (DE-588)4077852-6 (DE-588)4138606-1 (DE-588)4064324-4 (DE-588)4187413-4 (DE-588)4056995-0 (DE-588)4123623-3 |
| title | Theory of statistics |
| title_auth | Theory of statistics |
| title_exact_search | Theory of statistics |
| title_full | Theory of statistics Mark J. Schervish |
| title_fullStr | Theory of statistics Mark J. Schervish |
| title_full_unstemmed | Theory of statistics Mark J. Schervish |
| title_short | Theory of statistics |
| title_sort | theory of statistics |
| topic | Mathematical statistics sbt Mathematical statistics Schätztheorie (DE-588)4121608-8 gnd Auswahlfunktion (DE-588)4134349-9 gnd Statistischer Test (DE-588)4077852-6 gnd Entscheidungstheorie (DE-588)4138606-1 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Varianzanalyse (DE-588)4187413-4 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Mathematical statistics Schätztheorie Auswahlfunktion Statistischer Test Entscheidungstheorie Wahrscheinlichkeitsrechnung Varianzanalyse Statistik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006961950&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT schervishmarkj theoryofstatistics |