Statistical inference:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Pacific Grove, Calif.
Duxbury/Thomson Learning
2002
|
| Edition: | 2. ed., internat. student ed. |
| Series: | Duxbury advanced series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XXVIII, 660 S. graph. Darst. |
| ISBN: | 9780495391876 0495391875 |
Staff View
MARC
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| 100 | 1 | |a Casella, George |d 1951-2012 |e Verfasser |0 (DE-588)170529525 |4 aut | |
| 245 | 1 | 0 | |a Statistical inference |c George Casella ; Roger L. Berger |
| 250 | |a 2. ed., internat. student ed. | ||
| 264 | 1 | |a Pacific Grove, Calif. |b Duxbury/Thomson Learning |c 2002 | |
| 300 | |a XXVIII, 660 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
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Record in the Search Index
| _version_ | 1804138081027096576 |
|---|---|
| adam_text | Contents
1
Probability Theory
1
1.1
Set Theory
1
1.2
Basics of Probability Theory
5
1.2.1
Axiomatic Foundations
5
1.2.2
The Calculus of Probabilities
9
1.2.3
Counting
13
1.2.4
Enumerating Outcomes
16
1.3
Conditional Probability and Independence
20
1.4
Random Variables
27
1.5
Distribution Functions
29
1.6
Density and Mass Functions
34
1.7
Exercises
37
1.8
Miscellanea
44
2
Transformations and Expectations
47
2.1
Distributions of Functions of a Random Variable
47
2.2
Expected Values
55
2.3
Moments and Moment Generating Functions
59
2.4
Differentiating Under an Integral Sign
68
2.5
Exercises
76
2.6
Miscellanea
82
3
Common Families of Distributions
85
3.1
Introduction
85
3.2
Discrete Distributions
85
3.3
Continuous Distributions
98
3.4
Exponential Families 111
3.5
Location and Scale Families
116
CONTENTS
3.6
Inequalities and Identities
121
3.6.1
Probability Inequalities
122
3.6.2
Identities
123
3.7
Exercises
127
3.8
Miscellanea
135
Multiple Random Variables
139
4.1
Joint and Marginal Distributions
139
4.2
Conditional Distributions and Independence
147
4.3
Bivariate Transformations
156
4.4
Hierarchical Models and Mixture Distributions
162
4.5
Covariance and Correlation
169
4.6
Multivariate Distributions
177
4.7
Inequalities
186
4.7.1
Numerical Inequalities
186
4.7.2
Functional Inequalities
189
4.8
Exercises
192
4.9
Miscellanea
203
Properties of a Random Sample
207
5.1
Basic Concepts of Random Samples
207
5.2
Sums of Random Variables from a Random Sample
211
5.3
Sampling from the Normal Distribution
218
5.3.1
Properties of the Sample Mean and Variance
218
5.3.2
The Derived Distributions: Student s
t
and Snedecor s
F
222
5.4
Order Statistics
226
5.5
Convergence Concepts
232
5.5.1
Convergence in Probability
232
5.5.2
Almost Sure Convergence
234
5.5.3
Convergence in Distribution
235
5.5.4
The Delta Method
240
5.6
Generating a Random Sample
245
5.6.1
Direct Methods
247
5.6.2
Indirect Methods
251
5.6.3
The Accept/Reject Algorithm
253
5.7
Exercises
255
5.8
Miscellanea
267
.
Principles of Data Reduction
271
6.1
Introduction
271
6.2
The Sufficiency Principle
272
6.2.1
Sufficient Statistics
272
6.2.2
Minimal Sufficient Statistics
279
6.2.3
Ancillary Statistics
282
6.2.4
Sufficient, Ancillary, and Complete Statistics
284
CONTENTS xv
6.3
The Likelihood Principle
290
6.3.1
The Likelihood Function
290
6.3.2
The Formal Likelihood Principle
292
6.4
The Equivariance Principle
296
6.5
Exercises
300
6.6
Miscellanea
307
Point Estimation
311
7.1
Introduction
311
7.2
Methods of Finding Estimators
312
7.2.1
Method of Moments
312
7.2.2
Maximum Likelihood Estimators
315
7.2.3
Bayes
Estimators
324
7.2.4
The EM Algorithm
326
7.3
Methods of Evaluating Estimators
330
7.3.1
Mean Squared Error
330
7.3.2
Best Unbiased Estimators
334
7.3.3
Sufficiency and Unbiasedness
342
7.3.4
Loss Function Optimality
348
7.4
Exercises
355
7.5
Miscellanea
367
Hypothesis Testing
373
8.1
Introduction
373
8.2
Methods of Finding Tests
374
8.2.1
Likelihood Ratio Tests
374
8.2.2
Bayesian Tests
379
8.2.3
Union-Intersection and Intersection-Union Tests
380
8.3
Methods of Evaluating Tests
382
8.3.1
Error Probabilities and the Power Function
382
8.3.2
Most Powerful Tests
387
8.3.3
Sizes of Union-Intersection and Intersection-Union Tests
394
8.3.4
p-Values
397
8.3.5
Loss Function Optimality
400
8.4
Exercises
402
8.5
Miscellanea
413
Interval Estimation
417
9.1
Introduction
417
9.2
Methods of Finding Interval Estimators
420
9.2.1
Inverting a Test Statistic
420
9.2.2
Pivotal Quantities
427
9.2.3
Pivoting the CDF
430
9.2.4
Bayesian Intervals
435
xvi CONTENTS
9.3
Methods of Evaluating Interval Estimators
440
9.3.1
Size and Coverage Probability
440
9.3.2
Test-Related Optimality
444
9.3.3
Bayesian Optimality
447
9.3.4
Loss Function Optimality
449
9.4
Exercises
451
9.5
Miscellanea
463
10
Asymptotic Evaluations
467
10.1
Point Estimation
467
10.1.1
Consistency
467
10.1.2
Efficiency
470
10.1.3
Calculations and Comparisons
473
10.1.4
Bootstrap Standard Errors
478
10.2
Robustness
481
10.2.1
The Mean and the Median
482
10.2.2
M-Estimators
484
10.3
Hypothesis Testing
488
10.3.1
Asymptotic Distribution of LRTs
488
10.3.2
Other Large-Sample Tests
492
10.4
Interval Estimation
496
10.4.1
Approximate Maximum Likelihood Intervals
496
10.4.2
Other Large-Sample Intervals
499
10.5
Exercises
504
10.6
Miscellanea
515
11
Analysis of Variance and Regression
521
11.1
Introduction
521
11.2
Oneway Analysis of Variance
522
11.2.1
Model and Distribution Assumptions
524
11.2.2
The Classic ANOVA Hypothesis
525
11.2.3
Inferences Regarding Linear Combinations of Means
527
11.2.4
The ANOVA
F
Test
530
11.2.5
Simultaneous Estimation of Contrasts
534
11.2.6
Partitioning Sums of Squares
536
11.3
Simple Linear Regression
539
11.3.1
Least Squares: A Mathematical Solution
542
11.3.2
Best Linear Unbiased Estimators: A Statistical Solution
544
11.3.3
Models and Distribution Assumptions
548
11.3.4
Estimation and Testing with Normal Errors
550
11.3.5
Estimation and Prediction at a Specified
χ
=
xQ
557
11.3.6
Simultaneous Estimation and Confidence Bands
559
11.4
Exercises
563
11.5
Miscellanea
572
CONTENTS xvii
12 Regression Models 577
12.1
Introduction
577
12.2 Regression
with Errors in
Variables 577
12.2.1
Functional and Structural Relationships
579
12.2.2
A Least Squares Solution
581
12.2.3
Maximum Likelihood Estimation
583
12.2.4
Confidence Sets
588
12.3
Logistic Regression
591
12.3.1
The Model
591
12.3.2
Estimation
593
12.4
Robust Regression
597
12.5
Exercises
602
12.6
Miscellanea
608
Appendix: Computer Algebra
613
Table of Common Distributions
621
References
629
Author Index
645
Subject Index
649
|
| adam_txt |
Contents
1
Probability Theory
1
1.1
Set Theory
1
1.2
Basics of Probability Theory
5
1.2.1
Axiomatic Foundations
5
1.2.2
The Calculus of Probabilities
9
1.2.3
Counting
13
1.2.4
Enumerating Outcomes
16
1.3
Conditional Probability and Independence
20
1.4
Random Variables
27
1.5
Distribution Functions
29
1.6
Density and Mass Functions
34
1.7
Exercises
37
1.8
Miscellanea
44
2
Transformations and Expectations
47
2.1
Distributions of Functions of a Random Variable
47
2.2
Expected Values
55
2.3
Moments and Moment Generating Functions
59
2.4
Differentiating Under an Integral Sign
68
2.5
Exercises
76
2.6
Miscellanea
82
3
Common Families of Distributions
85
3.1
Introduction
85
3.2
Discrete Distributions
85
3.3
Continuous Distributions
98
3.4
Exponential Families 111
3.5
Location and Scale Families
116
CONTENTS
3.6
Inequalities and Identities
121
3.6.1
Probability Inequalities
122
3.6.2
Identities
123
3.7
Exercises
127
3.8
Miscellanea
135
Multiple Random Variables
139
4.1
Joint and Marginal Distributions
139
4.2
Conditional Distributions and Independence
147
4.3
Bivariate Transformations
156
4.4
Hierarchical Models and Mixture Distributions
162
4.5
Covariance and Correlation
169
4.6
Multivariate Distributions
177
4.7
Inequalities
186
4.7.1
Numerical Inequalities
186
4.7.2
Functional Inequalities
189
4.8
Exercises
192
4.9
Miscellanea
203
Properties of a Random Sample
207
5.1
Basic Concepts of Random Samples
207
5.2
Sums of Random Variables from a Random Sample
211
5.3
Sampling from the Normal Distribution
218
5.3.1
Properties of the Sample Mean and Variance
218
5.3.2
The Derived Distributions: Student's
t
and Snedecor's
F
222
5.4
Order Statistics
226
5.5
Convergence Concepts
232
5.5.1
Convergence in Probability
232
5.5.2
Almost Sure Convergence
234
5.5.3
Convergence in Distribution
235
5.5.4
The Delta Method
240
5.6
Generating a Random Sample
245
5.6.1
Direct Methods
247
5.6.2
Indirect Methods
251
5.6.3
The Accept/Reject Algorithm
253
5.7
Exercises
255
5.8
Miscellanea
267
.
Principles of Data Reduction
271
6.1
Introduction
271
6.2
The Sufficiency Principle
272
6.2.1
Sufficient Statistics
272
6.2.2
Minimal Sufficient Statistics
279
6.2.3
Ancillary Statistics
282
6.2.4
Sufficient, Ancillary, and Complete Statistics
284
CONTENTS xv
6.3
The Likelihood Principle
290
6.3.1
The Likelihood Function
290
6.3.2
The Formal Likelihood Principle
292
6.4
The Equivariance Principle
296
6.5
Exercises
300
6.6
Miscellanea
307
Point Estimation
311
7.1
Introduction
311
7.2
Methods of Finding Estimators
312
7.2.1
Method of Moments
312
7.2.2
Maximum Likelihood Estimators
315
7.2.3
Bayes
Estimators
324
7.2.4
The EM Algorithm
326
7.3
Methods of Evaluating Estimators
330
7.3.1
Mean Squared Error
330
7.3.2
Best Unbiased Estimators
334
7.3.3
Sufficiency and Unbiasedness
342
7.3.4
Loss Function Optimality
348
7.4
Exercises
355
7.5
Miscellanea
367
Hypothesis Testing
373
8.1
Introduction
373
8.2
Methods of Finding Tests
374
8.2.1
Likelihood Ratio Tests
374
8.2.2
Bayesian Tests
379
8.2.3
Union-Intersection and Intersection-Union Tests
380
8.3
Methods of Evaluating Tests
382
8.3.1
Error Probabilities and the Power Function
382
8.3.2
Most Powerful Tests
387
8.3.3
Sizes of Union-Intersection and Intersection-Union Tests
394
8.3.4
p-Values
397
8.3.5
Loss Function Optimality
400
8.4
Exercises
402
8.5
Miscellanea
413
Interval Estimation
417
9.1
Introduction
417
9.2
Methods of Finding Interval Estimators
420
9.2.1
Inverting a Test Statistic
420
9.2.2
Pivotal Quantities
427
9.2.3
Pivoting the CDF
430
9.2.4
Bayesian Intervals
435
xvi CONTENTS
9.3
Methods of Evaluating Interval Estimators
440
9.3.1
Size and Coverage Probability
440
9.3.2
Test-Related Optimality
444
9.3.3
Bayesian Optimality
447
9.3.4
Loss Function Optimality
449
9.4
Exercises
451
9.5
Miscellanea
463
10
Asymptotic Evaluations
467
10.1
Point Estimation
467
10.1.1
Consistency
467
10.1.2
Efficiency
470
10.1.3
Calculations and Comparisons
473
10.1.4
Bootstrap Standard Errors
478
10.2
Robustness
481
10.2.1
The Mean and the Median
482
10.2.2
M-Estimators
484
10.3
Hypothesis Testing
488
10.3.1
Asymptotic Distribution of LRTs
488
10.3.2
Other Large-Sample Tests
492
10.4
Interval Estimation
496
10.4.1
Approximate Maximum Likelihood Intervals
496
10.4.2
Other Large-Sample Intervals
499
10.5
Exercises
504
10.6
Miscellanea
515
11
Analysis of Variance and Regression
521
11.1
Introduction
521
11.2
Oneway Analysis of Variance
522
11.2.1
Model and Distribution Assumptions
524
11.2.2
The Classic ANOVA Hypothesis
525
11.2.3
Inferences Regarding Linear Combinations of Means
527
11.2.4
The ANOVA
F
Test
530
11.2.5
Simultaneous Estimation of Contrasts
534
11.2.6
Partitioning Sums of Squares
536
11.3
Simple Linear Regression
539
11.3.1
Least Squares: A Mathematical Solution
542
11.3.2
Best Linear Unbiased Estimators: A Statistical Solution
544
11.3.3
Models and Distribution Assumptions
548
11.3.4
Estimation and Testing with Normal Errors
550
11.3.5
Estimation and Prediction at a Specified
χ
=
xQ
557
11.3.6
Simultaneous Estimation and Confidence Bands
559
11.4
Exercises
563
11.5
Miscellanea
572
CONTENTS xvii
12 Regression Models 577
12.1
Introduction
577
12.2 Regression
with Errors in
Variables 577
12.2.1
Functional and Structural Relationships
579
12.2.2
A Least Squares Solution
581
12.2.3
Maximum Likelihood Estimation
583
12.2.4
Confidence Sets
588
12.3
Logistic Regression
591
12.3.1
The Model
591
12.3.2
Estimation
593
12.4
Robust Regression
597
12.5
Exercises
602
12.6
Miscellanea
608
Appendix: Computer Algebra
613
Table of Common Distributions
621
References
629
Author Index
645
Subject Index
649 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Casella, George 1951-2012 Berger, Roger L. 1951- |
| author_GND | (DE-588)170529525 (DE-588)1158102003 |
| author_facet | Casella, George 1951-2012 Berger, Roger L. 1951- |
| author_role | aut aut |
| author_sort | Casella, George 1951-2012 |
| author_variant | g c gc r l b rl rlb |
| building | Verbundindex |
| bvnumber | BV035109234 |
| classification_rvk | QH 231 SK 830 |
| classification_tum | MAT 625f |
| ctrlnum | (OCoLC)500794151 (DE-599)BVBBV035109234 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed., internat. student ed. |
| format | Book |
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| id | DE-604.BV035109234 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:16:51Z |
| indexdate | 2024-07-09T21:22:31Z |
| institution | BVB |
| isbn | 9780495391876 0495391875 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016777093 |
| oclc_num | 500794151 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-898 DE-BY-UBR DE-945 DE-M347 DE-91G DE-BY-TUM DE-29T DE-91 DE-BY-TUM DE-634 DE-573 DE-703 |
| owner_facet | DE-355 DE-BY-UBR DE-898 DE-BY-UBR DE-945 DE-M347 DE-91G DE-BY-TUM DE-29T DE-91 DE-BY-TUM DE-634 DE-573 DE-703 |
| physical | XXVIII, 660 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Duxbury/Thomson Learning |
| record_format | marc |
| series2 | Duxbury advanced series |
| spelling | Casella, George 1951-2012 Verfasser (DE-588)170529525 aut Statistical inference George Casella ; Roger L. Berger 2. ed., internat. student ed. Pacific Grove, Calif. Duxbury/Thomson Learning 2002 XXVIII, 660 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Duxbury advanced series Hier auch später erschienene, unveränderte Nachdrucke Inferenzstatistik Inferenzstatistik (DE-588)4247120-5 gnd rswk-swf Statistischer Test (DE-588)4077852-6 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Inferenzstatistik (DE-588)4247120-5 s DE-604 Statistischer Test (DE-588)4077852-6 s 1\p DE-604 Statistik (DE-588)4056995-0 s 2\p DE-604 Berger, Roger L. 1951- Verfasser (DE-588)1158102003 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016777093&sequence=000002&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 |
| spellingShingle | Casella, George 1951-2012 Berger, Roger L. 1951- Statistical inference Inferenzstatistik Inferenzstatistik (DE-588)4247120-5 gnd Statistischer Test (DE-588)4077852-6 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4247120-5 (DE-588)4077852-6 (DE-588)4056995-0 |
| title | Statistical inference |
| title_auth | Statistical inference |
| title_exact_search | Statistical inference |
| title_exact_search_txtP | Statistical inference |
| title_full | Statistical inference George Casella ; Roger L. Berger |
| title_fullStr | Statistical inference George Casella ; Roger L. Berger |
| title_full_unstemmed | Statistical inference George Casella ; Roger L. Berger |
| title_short | Statistical inference |
| title_sort | statistical inference |
| topic | Inferenzstatistik Inferenzstatistik (DE-588)4247120-5 gnd Statistischer Test (DE-588)4077852-6 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Inferenzstatistik Statistischer Test Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016777093&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT casellageorge statisticalinference AT bergerrogerl statisticalinference |