Statistical hypothesis testing: theory and methods
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2008
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 307 S. graph. Darst. |
| ISBN: | 9789812814364 9812814361 |
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MARC
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Record in the Search Index
| _version_ | 1804140026518306816 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
PREFACE VII
1. STATISTICAL SPACES 1
1.1 BASIC PROPERTIES OF STATISTICAL SPACES 2
1.1.1 MEASURE IN STATISTICAL SPACES 2
1.1.2 EQUIVALENCE AND DIVISIBILITY OF FAMILY OF PROBABILITY
DISTRIBUTIONS 8
1.2 CONDITIONAL PROBABILITY AND SUFFICIENT STATISTICS 12
1.2.1 STATISTICS AND RANDOM VARIABLES 13
1.2.2 CONDITIONAL PROBABILITY 15
1.2.3 SUFFICIENT STATISTICS 20
1.3 EXPONENTIAL FAMILY AND COMPLETENESS 27
1.3.1 EXPONENTIAL FAMILY 28
1.3.2 COMPLETENESS 30
1.3.3 SUFFICIENCY AND COMPLETENESS 34
1.3.4 ANCILLARY STATISTICS 35
1.4 ESTIMATION METHODS BASED ON STATISTICAL SPACE 37
1.4.1 MOMENT ESTIMATION AND MEDIAN ESTIMATION . .. 37 1.4.2 MAXIMUM
LIKELIHOOD ESTIMATORS 40
1.4.3 QUALITY OF ESTIMATORS 46
1.4.4 COMPARISON OF ESTIMATORS 51
1.4.5 NONPARAMETRIC MLE FOR POPULATION CDF 55
1.5 PROBLEMS 58
2. METHODS OF STATISTICAL TESTS 65
2.1 INTRODUCTION: BACKGROUND OF PROBLEM 65
IMAGE 2
2.2 LIKELIHOOD RATIO TESTS 72
2.2.1 THE LIKELIHOOD RATIO METHODS 72
2.2.2 LRT S LIMITING DISTRIBUTION 79
2.3 TESTS OF GOODNESS-OF-FIT 86
2.3.1 LIMITING DISTRIBUTION 87
2.3.2 TEST OF INDEPENDENCE IN TWO-WAY CONTINGENCY TABLE 90
2.3.3 TEST OF INDEPENDENCE IN THREE-WAY CONTINGENCY TABLE 92
2.3.4 GOODNESS-OF-FIT TEST OF DISTRIBUTION FUNCTION . . 95 2.4 SIGN
TESTS AND RANK TESTS 96
2.4.1 SIGN TESTS 97
2.4.2 WILCOXON SIGNED RANK TESTS 98
2.4.3 WILCOXON RANK TESTS 102
2.5 U-I TESTS 104
2.6 EMPIRICAL LIKELIHOOD-RATIO TESTS 108
2.7 PROBLEMS 112
3. THE COMPARISON OF TEST STATISTICS 117
3.1 PROBABILITY OF TWO TYPES OF ERROR IN HYPOTHESIS TEST . . 117 3.2
NEYMAN-PEARSON FUNDAMENTAL LEMMA 121
3.3 UNBIASED TEST 133
3.4 COMPARING POWER FUNCTIONS 141
3.4.1 TEST PROCEDURES 141
3.4.2 POWER FUNCTIONS AND THEIR COMPARISON 145
3.5 COMPARING ROBUSTNESS 148
3.5.1 EFFICIENCY OF TESTS 148
3.5.2 ASYMPTOTIC RELATIVE EFFICIENCY 151
3.6 INTERVAL ESTIMATION BASED ON TEST 154
3.6.1 INTERVAL ESTIMATION AND ACCEPTANCE REGION . . .. 156 3.6.2
UNIFORMLY MOST ACCURATE CONFIDENCE INTERVAL . . 158 3.6.3 UNIFORMLY MOST
ACCURATE UNBIASED CONFIDENCE INTERVAL 160
3.6.4 UNIFORMLY MOST ACCURACY AND INTERVAL LENGTH . . 165 3.7 PROBLEMS
166
4. PARAMETRIC TESTS FOR SIMPLE MODELS 175
4.1 ONE-FACTOR MODEL: ANALYSIS OF VARIANCE 175
IMAGE 3
4.2 ONE-FACTOR MODEL: MULTIPLE COMPARISONS 181
4.2.1 MULTIPLE COMPARISONS 182
4.2.2 GENERALIZED MULTIPLE COMPARISONS 186
4.2.3 THE FALSE DISCOVERY RATE PROCEDURE 189
4.3 ONE-FACTOR MODEL: TREND TESTS 191
4.3.1 LINEARITY TESTS 192
4.3.2 LIKELIHOOD RATIO TEST 197
4.3.3 LINEAR RANK TESTS 210
4.4 MULTI-FACTOR MODEL: ANALYSIS OF VARIANCE 213
4.4.1 MODEL WITHOUT INTERACTION EFFECTS 213
4.4.2 MODEL WITH INTERACTION EFFECTS 217
4.5 MULTI-FACTOR MODEL: LOG-LINEAR MODELS 219
4.5.1 TWO-DIMENSIONAL CONTINGENCY TABLE 219
4.5.2 THREE-DIMENSIONAL CONTINGENCY TABLE 223
4.5.3 ANCILLARY PARAMETER MODEL 226
4.6 PROBLEMS 227
5. PARAMETRIC TESTS FOR REGRESSION MODELS 235
5.1 LINEAR MODELS 235
5.1.1 ESTABLISHMENT OF MODEL 235
5.1.2 ESTIMATING AND TESTING THE PARAMETERS 240
5.1.3 CENTRALIZATION 245
5.2 REGRESSION MODELS 248
5.2.1 REGRESSION MODEL AND LINEAR MODEL 248
5.2.2 ERRORS-IN-VARIABLES MODEL 251
5.3 LOGISTIC REGRESSION MODELS 256
5.3.1 ONE-VARIABLE CASE 257
5.3.2 MULTIVARIABLE CASE 263
5.4 TIME SERIES: TREND TERM MODELS 264
5.5 TIME SERIES: AUTOREGRESSIVE MODELS 271
5.5.1 RANDOM WALK AND BROWNIAN MOTION 271
5.5.2 AUTOREGRESSIVE MODEL 273
5.6 GRANGER CAUSALITY TESTS 281
5.6.1 GRANGER CAUSALITY 281
5.6.2 INTEGRATION OF ORDER D 284
5.6.3 REAL DATA ANALYSIS 286
5.7 PROBLEMS 288
IMAGE 4
BIBLIOGRAPHY 297
INDEX 303
|
| any_adam_object | 1 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.56 |
| dewey-search | 519.56 |
| dewey-sort | 3519.56 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035740873 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:53:26Z |
| institution | BVB |
| isbn | 9789812814364 9812814361 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018017291 |
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| physical | XII, 307 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Shi, Ning-Zhong Verfasser aut Statistical hypothesis testing theory and methods Ning-Zhong Shi & Jian Tao Singapore [u.a.] World Scientific 2008 XII, 307 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistical hypothesis testing Statistischer Test (DE-588)4077852-6 gnd rswk-swf Statistischer Test (DE-588)4077852-6 s DE-604 Tao, Jian Verfasser aut SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018017291&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shi, Ning-Zhong Tao, Jian Statistical hypothesis testing theory and methods Statistical hypothesis testing Statistischer Test (DE-588)4077852-6 gnd |
| subject_GND | (DE-588)4077852-6 |
| title | Statistical hypothesis testing theory and methods |
| title_auth | Statistical hypothesis testing theory and methods |
| title_exact_search | Statistical hypothesis testing theory and methods |
| title_full | Statistical hypothesis testing theory and methods Ning-Zhong Shi & Jian Tao |
| title_fullStr | Statistical hypothesis testing theory and methods Ning-Zhong Shi & Jian Tao |
| title_full_unstemmed | Statistical hypothesis testing theory and methods Ning-Zhong Shi & Jian Tao |
| title_short | Statistical hypothesis testing |
| title_sort | statistical hypothesis testing theory and methods |
| title_sub | theory and methods |
| topic | Statistical hypothesis testing Statistischer Test (DE-588)4077852-6 gnd |
| topic_facet | Statistical hypothesis testing Statistischer Test |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018017291&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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