Parametric statistical inference: basic theory and modern approaches
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Oxford [u.a.]
Pergamon Press
1981
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | International series in nonlinear mathematics
4 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000603556&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVI, 387 S. |
| ISBN: | 0080264689 |
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| 245 | 1 | 0 | |a Parametric statistical inference |b basic theory and modern approaches |c by Shelemyahu Zacks |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Oxford [u.a.] |b Pergamon Press |c 1981 | |
| 300 | |a XVI, 387 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a International series in nonlinear mathematics |v 4 | |
| 490 | 0 | |a Pergamon international library. | |
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| 650 | 4 | |a Statistique - Science | |
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| 830 | 0 | |a International series in nonlinear mathematics |v 4 |w (DE-604)BV002809947 |9 4 | |
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Datensatz im Suchindex
| _version_ | 1819257917485875200 |
|---|---|
| adam_text | CONTENTS
LIST
OF
ILLUSTRATIONS
XIII
CHAPTER
1.
GENERAL
REVIEW
1
1.1
INTRODUCTION
1
1.2
STATISTICAL
MODELS,
DISTRIBUTION
FUNCTIONS
AND
THE
ESSENCE
OF
STATISTICAL
INFERENCE
2
1.3
THE
INFORMATION
IN
SAMPLES
AND
SUFFICIENT
STATISTICS
4
1.4
TESTING
STATISTICAL
HYPOTHESES
5
1.5
ESTIMATION
THEORY
6
1.6
THE
EFFICIENCY
OF
ESTIMATORS
8
1.7
CONFIDENCE
AND
TOLERANCE
INTERVALS
10
1.8
DECISION
THEORETIC
AND
BAYESIAN
APPROACH
IN
TESTING
AND
ESTIMATION
11
CHAPTER
2
BASIC
THEORY
OF
STATISTICAL
DISTRIBUTIONS
15
2.1
INTRODUCTORY
REMARKS
15
2.2
ELEMENTARY
PROPERTIES
OF
DISTRIBUTION
FUNCTIONS
16
2.2.1
DISCRETE
DISTRIBUTIONS
16
2.2.2
ABSOLUTELY
CONTINUOUS
DISTRIBUTIONS
17
2.2.3
INVERSE
FUNCTIONS
17
2.2.4
TRANSFORMATIONS
18
2.3
SOME
FAMILIES
OF
DISCRETE
DISTRIBUTIONS
19
2.3.1
BINOMIAL
DISTRIBUTIONS
19
2.3.2
HYPERGEOMETRIC
DISTRIBUTIONS
20
2.3.3
POISSON
DISTRIBUTIONS
20
2.3.4
GEOMETRIC,
PASCAL
AND
NEGATIVE
BINOMIAL
21
2.4
SOME
FAMILIES
OF
CONTINUOUS
DISTRIBUTIONS
22
2.4.1
RECTANGULAR
DISTRIBUTIONS
22
2.4.2
BETA
DISTRIBUTIONS
24
2.4.3
GAMMA
DISTRIBUTIONS
24
2.4.4
WEIBULL
AND
EXTREME
VALUE
DISTRIBUTIONS
25
2.4.5
NORMAL
DISTRIBUTIONS
26
2.4.6
NORMAL
APPROXIMATIONS
27
2.5
EXPECTATIONS,
MOMENTS
AND
GENERATING
FUNCTIONS
29
2.6
JOINT
DISTRIBUTIONS,
CONDITIONAL
DISTRIBUTIONS
AND
INDEPENDENCE
33
2.6.1
JOINT
DISTRIBUTIONS
33
2.6.2
CONDITIONAL
DISTRIBUTIONS
36
2.6.3
INDEPENDENCE
39
2.6.4
TRANSFORMATIONS
40
2.7
MOMENTS
AND
COVARIANCES
OF
LINEAR
FUNCTIONS
43
IX
X
PARAMETRIC
STATISTICAL
INFERENCE
2.8
DISCRETE
MULTIVARIATE
DISTRIBUTIONS
46
2.8.1
MULTINOMIAL
DISTRIBUTIONS
46
2.8.2
MULTIVARIATE
NEGATIVE
BINOMIAL
47
2.8.3
MULTIVARIATE
HYPERGEOMETRIC
48
2.9
MULTINORMAL
DISTRIBUTIONS
49
2.9.1
BASIC
THEORY
49
2.9.2
DISTRIBUTIONS
OF
SUBVECTORS
AND
DISTRIBUTIONS
OF
LINEAR
FORMS
50
2.9.3
INDEPENDENCE
OF
LINEAR
FORMS
53
2.9.4
NORMAL
PROBABILITY
TRANSFORMATIONS
53
2.10
DISTRIBUTIONS
OF
SYMMETRIC
QUADRATIC
FORMS
OF
NORMAL
VARIABLES
54
2.11
INDEPENDENCE
OF
LINEAR
AND
QUADRATIC
FORMS
OF
NORMAL
VARIABLES
57
2.12
THE
ORDER
STATISTICS
59
2.13
THE
T-DISTRIBUTIONS
61
2.14
THE
F-DISTRIBUTIONS
62
2.15
THE
DISTRIBUTION
OF
THE
SAMPLE
CORRELATION
65
2.16
LIMIT
THEOREMS
67
2.17
PROBLEMS
_
70
CHAPTER
3.
SUFFICIENT
STATISTICS
AND
THE
INFORMATION
IN
SAMPLES
84
3.1
INTRODUCTION
84
3.2
DEFINITIONS
AND
CHARACTERIZATION
OF
SUFFICIENT
STATISTICS
85
3.3
LIKELIHOOD
FUNCTIONS
AND
MINIMAL
SUFFICIENT
STATISTICS
90
3.4
SUFFICIENT
STATISTICS
AND
EXPONENTIAL
TYPE
FAMILIES
95
3.5
SUFFICIENCY
AND
COMPLETENESS
99
3.6
INFORMATION
FUNCTIONS
AND
SUFFICIENCY
103
3.6.1
THE
FISHER
INFORMATION
103
3.6.2
THE
KULLBACK-LEIBLER
INFORMATION
106
3.7
PROBLEMS
109
CHAPTER
4.
TESTING
STATISTICAL
HYPOTHESES
113
4.1
THE
GENERAL
FRAMEWORK
113
4.2
THE
NEYMAN-PEARSON
FUNDAMENTAL
LEMMA
118
4.3
TESTING
ONE-SIDED
COMPOSITE
HYPOTHESES
IN
MLR
MODELS
123
4.4
TESTING
TWO-SIDED
HYPOTHESES
IN
ONE-PARAMETER
EXPONENTIAL
FAMILIES
128
4.5
TESTING
COMPOSITE
HYPOTHESES
WITH
NUISANCE
PARAMETERS-
UNBIASED
TESTS
130
4.6
LIKELIHOOD
RATIO
TESTS
140
4.6..1
TESTING
IN
NORMAL
REGRESSION
THEORY
141
4.6.2
COMPARISON
OF
NORMAL
MEANS:
THE
ANALYSIS
OF
VARIANCE
144
4.7
THE
ANALYSIS
OF
CONTINGENCY
TABLES
149
4.7.1
THE
STRUCTURE
OF
MULTI-WAY
CONTINGENCY
TABLES
AND
THE
STATISTICAL
MODEL
149
4.7.2
TESTING
THE
SIGNIFICANCE
OF
ASSOCIATION
149
4.7.3
THE
ANALYSIS
OF
2X2
TABLES
151
4.7.4
LIKELIHOOD
RATIO
TESTS
153
4.8
SEQUENTIAL
TESTING
OF
HYPOTHESES
154
4.8.1
THE
WALD
SEQUENTIAL
PROBABILITY
RATIO
TEST
155
4.8.2
SEQUENTIAL
TESTS
WITH
POWER
1
163
4.9
PROBLEMS
165
CHAPTER
5.
ESTIMATION
THEORY
176
5.1
GENERAL
DISCUSSION
176
5.2
UNBIASED
ESTIMATORS
177
5.2.1
GENERAL
DEFINITION
AND
EXAMPLE
177
5.2.2
MINIMUM
VARIANCE
UNBIASED
ESTIMATORS
179
5.2.3
BIAS
REDUCTION
BY
JACKKNIFING
182
5.3
BEST
LINEAR
UNBIASED
AND
LEAST
SQUARES
ESTIMATOR
184
5.3.1
BEST
LINEAR
UNBIASED
ESTIMATORS
OF
THE
MEAN
185
5.3.2
LEAST
SQUARES
AND
BEST
LINEAR
UNBIASED
ESTIMATORS
FOR
LINEAR
MODELS
186
CONTENTS
XI
5.3.3
BEST
LINEAR
COMBINATION
OF
ORDER
STATISTICS
192
5.4
STABILIZING
THE
LEAST
SQUARES
ESTIMATORS:
RIDGE
REGRESSION
194
5.5
MAXIMUM
LIKELIHOOD
ESTIMATION
198
5.5.1
DEFINITION
AND
EXAMPLES
198
5.5.2
MAXIMUM
LIKELIHOOD
ESTIMATORS
IN
EXPONENTIAL
TYPE
FAMILIES
200
5.5.3
THE
INVARIANCE
PRINCIPLE
201
5.5.4
NUMERICAL
PROBLEMS
202
5.5.5
ANOMALOUS
CASES
204
5.5.6
MLE
OF
THE
PARAMETERS
OF
TOLERANCE
DISTRIBUTIONS
207
5.6
EQUIVARIANT
ESTIMATORS
208
5.6.1
THE
STRUCTURE
OF
EQUIVARIANT
ESTIMATORS
208
5.6.2
MINIMUM
MSE
EQUIVARIANT
ESTIMATORS
210
5.6.3
THE
PITMAN
ESTIMATORS
213
5.7
MOMENT-EQUATIONS
ESTIMATORS
216
5.8
PRE-TEST
ESTIMATORS
220
5.9
ROBUST
ESTIMATORS
222
5.10
PROBLEMS
225
CHAPTER
6.
THE
EFFICIENCY
OF
ESTIMATORS
236
6.1
GENERAL
INTRODUCTION
236
6.2
THE
CRAMER-RAO
LOWER
BOUND
IN
REGULAR
ONE-PARAMETER
CASES
237
6.3
EXTENSION
OF
THE
CRAMER-RAO
INEQUALITY
TO
MULTIPARAMETER
CASES
240
6.4
GENERAL
INEQUALITIES
OF
THE
CRAMER-RAO
TYPE
242
6.5
THE
EFFICIENCY
OF
ESTIMATORS
IN
SMALL
SAMPLES
244
6.6
ASYMPTOTIC
PROPERTIES
OF
ESTIMATORS
246
6.6.1
THE
CONSISTENCY
OF
MLE
247
6.6.2
ASYMPTOTIC
NORMALITY
AND
EFFICIENCY
OF
MLE
248
6.7
SECOND-ORDER
ASYMPTOTIC
EFFICIENCY
252
6.8
MAXIMUM
PROBABILITY
ESTIMATORS
255
6.9
PROBLEMS
258
CHAPTER
7.
CONFIDENCE
AND
TOLERANCE
INTERVALS
262
7.1
GENERAL
INTRODUCTION
262
7.2
THE
CONSTRUCTION
OF
CONFIDENCE
INTERVALS
264
7.3
OPTIMAL
CONFIDENCE
INTERVALS
266
7.4
LARGE
SAMPLE
APPROXIMATIONS
272
7.5
TOLERANCE
INTERVALS
276
7.6
DISTRIBUTION-FREE
CONFIDENCE
AND
TOLERANCE
INTERVALS
278
7.7
SIMULTANEOUS
CONFIDENCE
INTERVALS
281
7.8
TWO-STAGE
AND
SEQUENTIAL
SAMPLING
FOR
FIXED-WIDTH
CONFIDENCE
INTERVALS
285
7.9
PROBLEMS
289
CHAPTER
8.
DECISION
THEORETIC
AND
BAYESIAN
APPROACH
IN
TESTING
AND
ESTIMATION
294
8.1
THE
BAYESIAN
FRAMEWORK
295
8.1.1
PRIOR,
POSTERIOR
AND
PREDICTIVE
DISTRIBUTIONS
295
8.1.2
BAYESIAN
INFORMATION
FUNCTIONS
297
8.1.3
NON-INFORMATIVE
AND
IMPROPER
PRIOR
DISTRIBUTIONS
299
8.1.4
RISK
FUNCTIONS,
BAYES
AND
MINIMAX
PROCEDURES
301
8.1.5
BAYES
SEQUENTIAL
DECISION
PROCEDURES
305
8.2
BAYESIAN
TESTING
OF
HYPOTHESES
307
8.2.1
TESTING
SIMPLE
HYPOTHESES
307
8.2.2
TESTING
COMPOSITE
HYPOTHESES
310
8.2.3
BAYES
SEQUENTIAL
TESTING
OF
HYPOTHESES
315
8.3
BAYESIAN
CONFIDENCE
INTERVALS
317
8.4
BAYES
AND
MINIMAX
ESTIMATORS
321
8.4.1
GENERAL
DISCUSSION
AND
EXAMPLES
321
8.4.2
BAYESIAN
ESTIMATES
IN
LINEAR
MODELS
323
8.4.3
MINIMAX
ESTIMATORS
325
XII
PARAMETRIC
STATISTICAL
INFERENCE
8.5
MINIMAX
RISK
AND
BAYES
EQUIVARIANT,
FORMAL
BAYES
AND
STRUCTURAL
ESTIMATORS
328
8.5.1
MINIMUM
RISK
AND
BAYES
EQUIVARIANT
ESTIMATORS
328
8.5.2
FORMAL
BAYES
ESTIMATORS
FOR
INVARIANT
PRIORS
333
8.5.3
EQUIVARIANT
ESTIMATORS
BASED
ON
STRUCTURAL
DISTRIBUTIONS
335
8.6
EMPIRICAL
BAYES
ESTIMATORS
339
8.7
THE
ADMISSIBILITY
OF
ESTIMATORS
342
8.7.1
SOME
BASIC
RESULTS
342
8.7.2
THE
INADMISSIBILITY
OF
SOME
COMMONLY
USED
ESTIMATORS
347
8.7.3
MINIMAX
AND
ADMISSIBLE
ESTIMATORS
OF
THE
LOCATION
PARAMETER
354
8.8
PROBLEMS
356
REFERENCES
364
INDEXES
380
AUTHOR
INDEX
380
SUBJECT
INDEX
384
|
| any_adam_object | 1 |
| author | Zacks, Shelemyahu 1932- |
| author_GND | (DE-588)172470951 |
| author_facet | Zacks, Shelemyahu 1932- |
| author_role | aut |
| author_sort | Zacks, Shelemyahu 1932- |
| author_variant | s z sz |
| building | Verbundindex |
| bvnumber | BV000997093 |
| callnumber-first | Q - Science |
| callnumber-label | QA276 |
| callnumber-raw | QA276 |
| callnumber-search | QA276 |
| callnumber-sort | QA 3276 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 230 SK 830 |
| ctrlnum | (OCoLC)7206033 (DE-599)BVBBV000997093 |
| 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 Wirtschaftswissenschaften |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV000997093 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T07:29:43Z |
| institution | BVB |
| isbn | 0080264689 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000603556 |
| oclc_num | 7206033 |
| open_access_boolean | |
| owner | DE-12 DE-19 DE-BY-UBM DE-739 DE-20 DE-706 DE-83 DE-188 |
| owner_facet | DE-12 DE-19 DE-BY-UBM DE-739 DE-20 DE-706 DE-83 DE-188 |
| physical | XVI, 387 S. |
| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| publisher | Pergamon Press |
| record_format | marc |
| series | International series in nonlinear mathematics |
| series2 | International series in nonlinear mathematics Pergamon international library. |
| spellingShingle | Zacks, Shelemyahu 1932- Parametric statistical inference basic theory and modern approaches International series in nonlinear mathematics Estimation statistique Probabilité Statistiek gtt Statistique - Science Statistik Mathematical statistics Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 |
| title | Parametric statistical inference basic theory and modern approaches |
| title_auth | Parametric statistical inference basic theory and modern approaches |
| title_exact_search | Parametric statistical inference basic theory and modern approaches |
| title_full | Parametric statistical inference basic theory and modern approaches by Shelemyahu Zacks |
| title_fullStr | Parametric statistical inference basic theory and modern approaches by Shelemyahu Zacks |
| title_full_unstemmed | Parametric statistical inference basic theory and modern approaches by Shelemyahu Zacks |
| title_short | Parametric statistical inference |
| title_sort | parametric statistical inference basic theory and modern approaches |
| title_sub | basic theory and modern approaches |
| topic | Estimation statistique Probabilité Statistiek gtt Statistique - Science Statistik Mathematical statistics Statistik (DE-588)4056995-0 gnd |
| topic_facet | Estimation statistique Probabilité Statistiek Statistique - Science Statistik Mathematical statistics |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000603556&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002809947 |
| work_keys_str_mv | AT zacksshelemyahu parametricstatisticalinferencebasictheoryandmodernapproaches |