Statistical inference:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2002
|
| Edition: | 2. ed. |
| Series: | Oxford science publications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 328 S. |
| ISBN: | 0198572263 |
Staff View
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| adam_text | STATISTICAL INFERENCE SECOND EDITION GEORGE CASELLA UNIVERSITY OF
FLORIDA ROGER L. BERGER NORTH CAROLINA STATE UNIVERSITY DUXBURY THOMSON
LEARNING AUSTRALIA * CANADA * MEXICO * SINGAPORE * SPAIN * UNITED
KINGDOM * UNITED STATES 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 X = 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 |
STATISTICAL INFERENCE SECOND EDITION GEORGE CASELLA UNIVERSITY OF
FLORIDA ROGER L. BERGER NORTH CAROLINA STATE UNIVERSITY DUXBURY THOMSON
LEARNING AUSTRALIA * CANADA * MEXICO * SINGAPORE * SPAIN * UNITED
KINGDOM * UNITED STATES 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 X = 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 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:34:28Z |
| indexdate | 2024-07-09T21:23:58Z |
| institution | BVB |
| isbn | 0198572263 |
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| publisher | Oxford Univ. Press |
| record_format | marc |
| series2 | Oxford science publications |
| spelling | Garthwaite, Paul H. Verfasser (DE-588)129573671 aut Statistical inference Paul Garthwaite, Ian Jolliffe and Byron Jones 2. ed. Oxford [u.a.] Oxford Univ. Press 2002 XI, 328 S. txt rdacontent n rdamedia nc rdacarrier Oxford science publications Mathematical statistics Statistische Schlussweise (DE-588)4182963-3 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Statistische Schlussweise (DE-588)4182963-3 s DE-604 Jolliffe, Ian T. Verfasser (DE-588)111240816 aut Jones, Byron 1951- Verfasser (DE-588)129573612 aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016848587&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Garthwaite, Paul H. Jolliffe, Ian T. Jones, Byron 1951- Statistical inference Mathematical statistics Statistische Schlussweise (DE-588)4182963-3 gnd |
| subject_GND | (DE-588)4182963-3 (DE-588)4123623-3 |
| title | Statistical inference |
| title_auth | Statistical inference |
| title_exact_search | Statistical inference |
| title_exact_search_txtP | Statistical inference |
| title_full | Statistical inference Paul Garthwaite, Ian Jolliffe and Byron Jones |
| title_fullStr | Statistical inference Paul Garthwaite, Ian Jolliffe and Byron Jones |
| title_full_unstemmed | Statistical inference Paul Garthwaite, Ian Jolliffe and Byron Jones |
| title_short | Statistical inference |
| title_sort | statistical inference |
| topic | Mathematical statistics Statistische Schlussweise (DE-588)4182963-3 gnd |
| topic_facet | Mathematical statistics Statistische Schlussweise Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016848587&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT garthwaitepaulh statisticalinference AT jolliffeiant statisticalinference AT jonesbyron statisticalinference |