Introduction to mathematical statistics:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston, Mass. ; Munich [u.a.]
Pearson
2011
|
| Edition: | 7. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Copyright 2013, CIP-Aufnahme 2013, Printleiste 2011 |
| Physical Description: | X, 694 S. graph. Darst. |
| ISBN: | 9780321795434 0321795431 |
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MARC
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| 245 | 1 | 0 | |a Introduction to mathematical statistics |c Robert V. Hogg ; Joseph W. McKean ; Allen T. Craig |
| 250 | |a 7. ed. | ||
| 264 | 1 | |a Boston, Mass. ; Munich [u.a.] |b Pearson |c 2011 | |
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Record in the Search Index
| _version_ | 1804148723202129920 |
|---|---|
| adam_text | Contents
Preface
ix
1
Probability and Distributions
1
1.1
Introduction
................................ 1
1.2
Set Theory
................................ 3
1.3
The Probability Set Function
...................... 10
1.4
Conditional Probability and Independence
............... 21
1.5
Random Variables
............................ 32
1.6
Discrete Random Variables
....................... 40
1.6.1
Transformations
......................... 42
1.7
Continuous Random Variables
...................... 44
1.7.1
Transformations
......................... 46
1.8
Expectation of a Random Variable
................... 52
1.9
Some Special Expectations
....................... 57
1.10
Important Inequalities
.......................... 68
2
Multivariate Distributions
73
2.1
Distributions of Two Random Variables
................ 73
2.1.1
Expectation
............................ 79
2.2
Transformations:
Divariate
Random Variables
............. 84
2.3
Conditional Distributions and Expectations
.............. 94
2.4
The Correlation Coefficient
....................... 102
2.5
Independent Random Variables
..................... 110
2.6
Extension to Several Random Variables
................ 117
2.6.1 *
Multivariate Variance-Covariance Matrix
........... 123
2.7
Transformations for Several Random Variables
............ 126
2.8
Linear Combinations of Random Variables
............... 134
3
Some Special Distributions
139
3.1
The Binomial and Related Distributions
................ 139
3.2
The
Poisson
Distribution
........................ 150
3.3
The
Γ, χ2,
and
β
Distributions
..................... 156
3.4
The Normal Distribution
......................... 168
3.4.1
Contaminated Normals
..................... 174
vi
Contents
3.5
The Multivariate Normal Distribution
................. 178
3.5.1
Applications
........................... 185
3.6
t- and F-Distributions
.......................... 189
3.6.1
The
ŕ-distribution
........................ 189
3.6.2
The ^-distribution
........................ 191
3.6.3
Student s Theorem
........................ 193
3.7
Mixture Distributions
.......................... 197
4
Some Elementary Statistical Inferences
203
4.1
Sampling and Statistics
......................... 203
4.1.1
Histogram Estimates of pmfs and pdfs
............. 207
4.2
Confidence Intervals
........................... 214
4.2.1
Confidence Intervals for Difference in Means
.......... 217
4.2.2
Confidence Interval for Difference in Proportions
....... 219
4.3
Confidence Intervals for Parameters of Discrete Distributions
.... 223
4.4
Order Statistics
.............................. 227
4.4.1
Quantiles
............................. 231
4.4.2
Confidence Intervals for Quantiles
............... 234
4.5
Introduction to Hypothesis Testing
................... 240
4.6
Additional Comments About Statistical Tests
............. 248
4.7
Chi-Square Tests
............................. 254
4.8
The Method of Monte Carlo
....................... 261
4.8.1
Accept-Reject Generation Algorithm
.............. 268
4.9
Bootstrap Procedures
.......................... 273
4.9.1
Percentile Bootstrap Confidence Intervals
........... 273
4.9.2
Bootstrap Testing Procedures
.................. 276
4.10
Tolerance Limits for Distributions
................... 284
5
Consistency and Limiting Distributions
289
5.1
Convergence in Probability
....................... 289
5.2
Convergence in Distribution
....................... 294
5.2.1
Bounded in Probability
..................... 300
5.2.2
Δ
-Method
.............................
301
5.2.3
Moment Generating Function Technique
............ 303
5.3
Central Limit Theorem
......................... 307
5.4 *
Extensions to Multivariate Distributions
............... 314
6
Maximum Likelihood Methods
321
6.1
Maximum Likelihood Estimation
.................... 321
6.2
Rao-Cramér
Lower Bound and Efficiency
............... 327
6.3
Maximum Likelihood Tests
....................... 341
6.4
Multiparameter Case: Estimation
.................... 350
6.5
Multiparameter Case: Testing
...................... 359
6.6
The EM Algorithm
............................ 367
Contents
7
Sufficiency
375
7.1
Measures of Quality of Estimators
................... 375
7.2
A Sufficient Statistic for a Parameter
.................. 381
7.3
Properties of a Sufficient Statistic
.................... 388
7.4
Completeness and Uniqueness
...................... 392
7.5
The Exponential Class of Distributions
................. 397
7.6
Functions of a Parameter
........................ 402
7.7
The Case of Several Parameters
..................... 407
7.8
Minimal Sufficiency and Ancillary Statistics
.............. 415
7.9
Sufficiency, Completeness, and Independence
............. 421
8
Optimal Tests of Hypotheses
429
8.1
Most Powerful Tests
........................... 429
8.2
Uniformly Most Powerful Tests
..................... 439
8.3
Likelihood Ratio Tests
.......................... 447
8.4
The Sequential Probability Ratio Test
................. 459
8.5
Minimax and Classification Procedures
................. 466
8.5.1
Minimax Procedures
....................... 466
8.5.2
Classification
........................... 469
9
Inferences About Normal Models
473
9.1
Quadratic Forms
............................. 473
9.2
One-Way ANOVA
............................ 478
9.3
Noncentral
χ2
and -F-Distributions
................... 484
9.4
Multiple Comparisons
.......................... 486
9.5
The Analysis of Variance
........................ 490
9.6
A Regression Problem
.......................... 497
9.7
A Test of Independence
......................... 506
9.8
The Distributions of Certain Quadratic Forms
............. 509
9.9
The Independence of Certain Quadratic Forms
............ 516
10
Nonparametric and Robust Statistics
525
10.1
Location Models
............................. 525
10.2
Sample Median and the Sign Test
.................... 528
10.2.1
Asymptotic Relative Efficiency
................. 533
10.2.2
Estimating Equations Based on the Sign Test
......... 538
10.2.3
Confidence Interval for the Median
............... 539
10.3
Signed-Rank Wilcoxon
.......................... 541
10.3.1
Asymptotic Relative Efficiency
................. 546
10.3.2
Estimating Equations Based on Signed-Rank Wilcoxon
. . . 549
10.3.3
Confidence Interval for the Median
............... 549
10.4
Mann-Whitney-Wilcoxon Procedure
.................. 551
10.4.1
Asymptotic Relative Efficiency
................. 555
10.4.2
Estimating Equations Based on the Mann-Whitney-Wilcoxon
556
10.4.3
Confidence Interval for the Shift Parameter
Δ
......... 557
10.5
General Rank Scores
........................... 559
viii Contents
10.5.1
Efficacy
..............................562
10.5.2
Estimating Equations Based on General Scores
........563
10.5.3
Optimization: Best Estimates
..................564
10.6
Adaptive Procedures
...........................571
10.7
Simple Linear Model
...........................576
10.8
Measures of Association
.........................581
10.8.1
Kendall s
τ
............................582
10.8.2
Spearman s Rho
.........................584
10.9
Robust Concepts
.............................588
10.9.1
Location Model
..........................589
10.9.2
Linear Model
...........................595
11
Bayesian Statistics
605
11.1
Subjective Probability
.......................... 605
11.2
Bayesian Procedures
........................... 608
11.2.1
Prior and Posterior Distributions
................ 609
11.2.2
Bayesian Point Estimation
.................... 612
11.2.3
Bayesian Interval Estimation
.................. 615
11.2.4
Bayesian Testing Procedures
.................. 616
11.2.5
Bayesian Sequential Procedures
................. 617
11.3
More Bayesian Terminology and Ideas
................. 619
11.4
Gibbs Sampler
.............................. 626
11.5
Modern Bayesian Methods
........................ 632
11.5.1
Empirical
Bayes
......................... 636
A Mathematical Comments
641
A.I Regularity Conditions
..........................641
A.
2
Sequences
.................................642
B R
Functions
645
С
Tables of Distributions
655
D
Lists of Common Distributions
665
E
References
669
F
Answers to Selected Exercises
673
Index
683
|
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| edition | 7. ed. |
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| spelling | Hogg, Robert V. ca. 20. Jh. Verfasser (DE-588)119507951 aut Introduction to mathematical statistics Robert V. Hogg ; Joseph W. McKean ; Allen T. Craig 7. ed. Boston, Mass. ; Munich [u.a.] Pearson 2011 X, 694 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Copyright 2013, CIP-Aufnahme 2013, Printleiste 2011 Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Statistik (DE-588)4056995-0 s SWB McKean, Joseph W. 1944- Verfasser (DE-588)124200540 aut Craig, Allen T. 1905-1978 Verfasser (DE-588)172027195 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024657520&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hogg, Robert V. ca. 20. Jh McKean, Joseph W. 1944- Craig, Allen T. 1905-1978 Introduction to mathematical statistics Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4151278-9 |
| title | Introduction to mathematical statistics |
| title_auth | Introduction to mathematical statistics |
| title_exact_search | Introduction to mathematical statistics |
| title_full | Introduction to mathematical statistics Robert V. Hogg ; Joseph W. McKean ; Allen T. Craig |
| title_fullStr | Introduction to mathematical statistics Robert V. Hogg ; Joseph W. McKean ; Allen T. Craig |
| title_full_unstemmed | Introduction to mathematical statistics Robert V. Hogg ; Joseph W. McKean ; Allen T. Craig |
| title_short | Introduction to mathematical statistics |
| title_sort | introduction to mathematical statistics |
| topic | Statistik (DE-588)4056995-0 gnd |
| topic_facet | Statistik Einführung |
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