Nonparametric statistical inference:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2011
|
| Edition: | 5. ed. |
| Series: | Statistics: textbooks & monographs
A Chapman & Hall book |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XX, 630 S. graph. Darst. |
| ISBN: | 9781420077612 |
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| 100 | 1 | |a Gibbons, Jean Dickinson |d 1938- |e Verfasser |0 (DE-588)132991373 |4 aut | |
| 245 | 1 | 0 | |a Nonparametric statistical inference |c Jean Dickinson Gibbons ; Subhabrata Chakraborti |
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| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2011 | |
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| adam_text | Titel: Nonparametric statistical inference
Autor: Gibbons, Jean Dickinson
Jahr: 2011
Contents
Preface to the Fifth Edition..............................................................................xvii
1. Introduction and Fundamentals..................................................................1
1.1 Introduction...........................................................................................1
1.2 Fundamental Statistical Concepts......................................................7
1.2.1 Basic Definitions......................................................................8
1.2.2 Moments of Linear Combinations of Random
Variables.................................................................................10
1.2.3 Probability Functions............................................................10
1.2.4 Distributions of Functions of Random Variables
Using the Method of lacobians...........................................15
1.2.5 Chebyshev s Inequality........................................................16
1.2.6 Central Limit Theorem.........................................................16
1.2.7 Point and Interval Estimation.............................................17
1.2.8 Hypothesis Testing...............................................................18
1.2.9 P Value...................................................................................21
1.2.10 Consistency............................................................................22
1.2.11 Pitman Efficiency..................................................................23
1.2.12 Randomized Tests.................................................................25
1.2.13 Continuity Correction...........................................................26
2. Order Statistics, Quantiles, and Coverages............................................29
2.1 Introduction.........................................................................................29
2.2 Quantile Function...............................................................................30
2.3 Empirical Distribution Function.......................................................33
2.3.1 Empirical Quantile Function...............................................36
2.4 Statistical Properties of Order Statistics..........................................37
2.4.1 Cumulative Distribution Function of X(r)..........................37
2.4.2 Probability Density Function of X(r)...................................37
2.5 Probability-Integral Transformation................................................39
2.6 Joint Distribution of Order Statistics...............................................41
2.7 Distributions of the Median and Range..........................................46
2.7.1 Distribution of the Median.................................................. 46
2.7.2 Distribution of the Range....................................................48
2.8 Exact Moments of Order Statistics...................................................49
2.8.1 Jtth Moment about the Origin.............................................49
2.8.2 Covariance between X(r) and X(s).......................................50
2.9 Large-Sample Approximations to the Moments
of Order Statistics...............................................................................53
VC
Contents
2.10 Asymptotic Distribution of Order Statistics...................................56
2.11 Tolerance Limits for Distributions and Coverages.......................60
2.11.1 One-Sample Coverages........................................................62
2.11.2 Two-Sample Coverages........................................................63
2.11.3 Ranks, Block Frequencies, and Placements.......................64
2.12 Summary..............................................................................................66
Problems.........................................................................................................66
3. Tests of Randomness..................................................................................75
3.1 Introduction.........................................................................................75
3.2 Tests Based on the Total Number of Runs.....................................76
3.2.1 Exact Null Distribution of R................................................76
3.2.2 Moments of the Null Distribution of R.............................80
3.2.3 Asymptotic Null Distribution.............................................82
3.2.4 Discussion..............................................................................83
3.2.5 Applications...........................................................................83
3.3 Tests Based on the Length of the Longest Run.............................85
3.4 Runs Up and Down...........................................................................88
3.4.1 Applications...........................................................................93
3.5 A Test Based on Ranks......................................................................94
3.6 Summary.......................... ....................................................................96
Problems.........................................................................................................96
4. Tests of Goodness of Fit...........................................................................101
4.1 Introduction.......................................................................................101
4.2 The Chi-Square Goodness-of-Fit Test............................................102
4.3 The Kolmogorov-Smirnov (K-S) One-Sample Statistic..............108
4.4 Applications of the Kolmogorov-Smirnov (K-S)
One-Sample Statistics.......................................................................117
4.4.1 One-Sided Tests...................................................................120
4.4.2 Confidence Bands...............................................................121
4.4.3 Determination of Sample Size...........................................122
4.5 Lilliefors s Test for Normality........................................................126
4.6 Lilliefors s Test for the Exponential Distribution........................133
4.7 Anderson-Darling (A-D) Test........................................................137
4.8 Visual Analysis of Goodness of Fit................................................142
4.9 Summary............................................................................................146
Problems.......................................................................................................148
5. One-Sample and Paired-Sample Procedures........................................157
5.1 Introduction.......................................................................................157
5.2 Confidence Interval for a Population Quantile............................158
5.3 Hypothesis Testing for a Population Quantile............................164
Contents xi
5.4 The Sign Test and Confidence Interval
for the Median........................................................ ..........................168
5.4.1 P Value.................................................................................170
5.4.2 Normal Approximations....................................................170
5.4.3 Zero Differences............:.....................................................171
5.4.4 Power Function...................................................................171
5.4.5 Simulated Power.................................................................175
5.4.6 Sample Size Determination...............................................178
5.4.7 Confidence Interval for the Median.................................179
5.4.8 Problem of Zeros.................................................................180
5.4.9 Paired-Sample Procedures.................................................180
5.4.10 Applications.........................................................................182
5.5 Rank-Order Statistics.......................................................................189
5.6 Treatment of Ties in Rank Tests.....................................................193
5.6.1 Randomization....................................................................193
5.6.2 Midranks..............................................................................194
5.6.3 Average Statistic..................................................................194
5.6.4 Average Probability............................................................194
5.6.5 Least Favorable Statistic.....................................................194
5.6.6 Range of Probability...........................................................195
5.6.7 Omission of Tied Observations.........................................195
5.7 The Wilcoxon Signed-Rank Test and Confidence Interval........195
5.7.1 The Problem of Zero and Tied Differences.....................202
5.7.2 Power Function...................................................................203
5.7.3 Simulated Power.................................................................204
5.7.4 Sample Size rjetenrtination...............................................205
5.7.5 Conndence-Interval Procedures........................................207
5.7.6 Paired-Sample Procedures.................................................210
5.7.7 Use of Wilcoxon Statistics to Test for Symmetry...........211
5.7.8 Applications.........................................................................211
5.8 Summary............................................................................................217
Problems.......................................................................................................219
6. The General Two-Sample Problem........................................................227
6.1 Introduction.......................................................................................227
6.2 The Wald-Wolfowitz Runs Test....................................................231
6.2.1 The Problem of Ties............................................................233
6.2.2 Discussion............................................................................234
6.3 The Kolmogorov-Srrtirnov (K-S) Two-Sample Test...................234
6.3.1 One-Sided Alternatives......................................................238
6.3.2 Ties........................................................................................239
6.3.3 Discussion............................................................................239
6.3.4 Applications.........................................................................240
6.4 The Median Test...............................................................................241
6.4.1 Applications.........................................................................247
xii Contents
6.4.2 Confidence-Interval Procedure.........................................251
6.4.3 Power of the Median Test..................................................253
6.5 The Control Median Test................................................................256
6.5.1 Curtailed Sampling.............................................................257
6.5.2 Power of the Control Median Test...................................258
6.5.3 Discussion............................................................................259
6.5.4 Applications.........................................................................259
6.6 The Mann-Whitney U Test and Confidence Interval.................261
6.6.1 The Problem of Ties............................................................266
6.6.2 Confidence-Interval Procedure.........................................267
6.6.3 Sample Size Determination...............................................269
6.6.4 Discussion............................................................................269
6.7 Summary............................................................................................270
Problems.......................................................................................................271
7. Linear Rank Statistics and the General Two-Sample Problem........275
7.1 Introduction.......................................................................................275
7.2 Definition of Linear Rank Statistics...............................................275
7.3 Distribution Properties of Linear Rank Statistics........................277
7.4 Usefulness in Inference....................................................................286
Problems.......................................................................................................287
8. Linear Rank Tests for the Location Problem.......................................289
8.1 Introduction.......................................................................................289
8.2 The Wilcoxon Rank-Sum Test and Confidence Interval............290
8.2.1 Applications.........................................................................293
8.3 Other Location Tests........................................................................299
8.3.1 Terry-Hoeffding (Normal Scores) Test............................299
8.3.2 van der Waerden Test........................................................301
8.3.3 Percentile Modified Rank Tests........................................304
8.4 Summary............................................................................................305
Problems.......................................................................................................306
9. Linear Rank Tests for the Scale Problem.............................................311
9.1 Introduction.......................................................................................311
9.2 The Mood Test..................................................................................314
9.3 The Freund-Ansari-Bradley-David-Barton Tests......................316
9.4 The Siegel-Tukey Test.....................................................................320
9.5 The Klotz Normal-Scores Test........................................................322
9.6 The Percentile Modified Rank Tests for Scale..............................323
9.7 The Sukhatme Test...........................................................................323
9.8 Confidence-Interval Procedures.....................................................328
9.9 Other Tests for the Scale Problem..................................................329
9.10 Applications......................................................................................331
Contents xiii
9.11 Summary............................................................................................338
Problems.......................................................................................................340
10. Tests of the Equality of k Independent Samples................................343
10.1 Introduction.......................................................................................343
10.2 Extension of the Median Test.........................................................344
10.3 Extension of the Control Median Test...........................................350
10.4 The Kruskal-Wallis One-Way ANOVA
Test and Multiple Comparisons.....................................................353
10.4.1 Applications.........................................................................357
10.5 Other Rank-Test Statistics...............................................................362
10.6 Tests against Ordered Alternatives...............................................364
10.6.1 Applications.........................................................................368
10.7 Comparisons with a Control..........................................................371
10.7.1 Case I: 9X Known.................................................................372
10.7.2 Case II: Bx Unknown...........................................................373
10.7.3 Applications.........................................................................376
10.8 Summary............................................................................................377
Problems.......................................................................................................378
11. Measures of Association for Bivariate Samples..................................385
11.1 Introduction: Definition of Measures of Association
in a Bivariate Population.................................................................385
11.2 Kendall s Tau Coefficient................................................................389.
11.2.1 Null Distribution of T.........................................................395
11.2.2 The Large-Sample Nonnull Distribution
of Kendall s Statistic...........................................................399
11.2.3 Tied Observations...............................................................403
11.2.4 A Related Measure of Association
for Discrete Populations.....................................................405
11.2.5 Use of Kendall s Statistic to Test against Trend.............406
11.3 Spearman s Coefficient of Rank Correlation................................407
11.3.1 Exact Null Distribution of R..............................................409
11.3.2 Asymptotic Null Distribution of R...................................412
11.3.3 Testing the Null Hypothesis..............................................413
11.3.4 Tied Observations...............................................................413
11.3.5 Use of Spearman s R to Test against Trend....................416
11.4 The Relations between R and T; £(R), t, and p...........................416
11.5 Another Measure of Association....................................................422
11.6 Applications......................................................................................423
11.7 Summary............................................................................................428
Problems.......................................................................................................429
xiv Contents
12. Measures of Association in Multiple Classifications.........................437
12.1 Introduction.......................................................................................437
12.2 Friedman s Two-Way Analysis of Variance by Ranks
inak xn Table and Multiple Comparisons.................................440
12.2.1 Applications.........................................................................444
12.3 Page s Test for Ordered Alternatives............................................448
12.4 The Coefficient of Concordance for k Sets of
Rankings of n Objects......................................................................452
12.4.1 Relationship between W and Rank Correlation.............454
12.4.2 Tests of Significance Based on W.....................................455
12.4.3 Estimation of the True Preferential Order
of Objects..............................................................................457
12.4.4 Tied Observations...............................................................458
12.4.5 Applications.........................................................................459
12.5 The Coefficient of Concordance for k Sets
of Incomplete Rankings...................................................................461
12.5.1 Tests of Significance Based on W.....................................464
12.5.2 Tied Observations...............................................................466
12.5.3 Applications.........................................................................466
12.6 Kendall s Tau Coefficient for Partial Correlation........................467
12.6.1 Applications.........................................................................470
12.7 Summary............................................................................................471
Problems.......................................................................................................472
13. Asymptotic Relative Efficiency...............................................................479
13.1 Introduction.......................................................................................479
13.2 Theoretical Bases for Calculating the ARE...................................482
13.3 Examples of the Calculation of Efficacy and ARE......................487
13.3.1 One-Sample and Paired-Sample Problems.....................488
13.3.2 Two-Sample Location Problems.......................................493
13.3.3 Two-Sample Scale Problems . ............................................498
13.4 Summary............................................................................................502
Problems.......................................................................................................503
14. Analysis of Count Data............................................................................505
14.1 Introduction.......................................................................................505
14.2 Contingency Tables..........................................................................505
14.2.1 Contingency Coefficient.....................................................510
14.3 Some Special Results for k x 2 Contingency Tables....................513
14.4 Fisher s Exact Test............................................................................517
14.5 McNemar s Test................................................................................522
14.6 Analysis of Multinomial Data........................................................528
14.6.1 Ordered Categories.............................................................530
Contents
xv
14.7 Summary............................................................................................532
Problems.......................................................................................................533
15. Summary......................................................................................................539
Appendix of Tables.........................................................................................541
Table A Normal Distribution.................................................................542
Table B Chi-Square Distribution...........................................................543
Table C Cumulative Binomial Distribution.........................................544
Table D Total Number of Runs Distribution......................................557
Table E Runs Up and Down Distribution...........................................562
Table F Kolmogorov-Smirnov One-Sample Statistic........................565
Table G Binomial Distribution for 0 ? 0.5............................................566
Table H Probabilities for the Wilcoxon Signed-Rank Statistic..........567
Table I Kolmogorov-Smirnov Two-Sample Statistic.......................571
Table J Probabilities for the Wilcoxon Rank-Sum Statistic..............574
Table K Kruskal-Wallis Test Statistic...................................................582
Table L Kendall s Tau Statistic.............................................................583
Table M Spearman s Coefficient of Rank Correlation........................585
Table N Friedman s Analysis-of-Variance Statistic
and Kendall s Coefficient of Concordance...........................588
Table O Lilliefor s Test for Normal Distribution Critical Values.....589
Table P Significance Points of TXy.z for Kendall s Partial
Rank-Correlation Coefficient..................................................590
Table Q Page s L Statistic.......................................................................591
Table R Critical Values and Associated Probabilities for the
Jonckheere-Terpstra Test........................................................592
Table S Rank von Neumann Statistic..................................................595
Table T Lilliefors s Test for Exponential Distribution
Critical Values...........................................................................598
Answers to Selected Problems.......................................................................599
References...........................................................................................................605
Index....................................................................................................................621
|
| any_adam_object | 1 |
| author | Gibbons, Jean Dickinson 1938- Chakraborti, Subhabrata 1957- |
| author_GND | (DE-588)132991373 (DE-588)120879131 |
| author_facet | Gibbons, Jean Dickinson 1938- Chakraborti, Subhabrata 1957- |
| author_role | aut aut |
| author_sort | Gibbons, Jean Dickinson 1938- |
| author_variant | j d g jd jdg s c sc |
| building | Verbundindex |
| bvnumber | BV036653023 |
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| callnumber-label | QA278 |
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| callnumber-sort | QA 3278.8 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 830 SK 835 SK 840 SK 850 |
| ctrlnum | (OCoLC)705783707 (DE-599)BVBBV036653023 |
| 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 |
| edition | 5. ed. |
| format | Book |
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| genre | 1\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV036653023 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:44:59Z |
| institution | BVB |
| isbn | 9781420077612 |
| language | English |
| lccn | 2010014490 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020572504 |
| oclc_num | 705783707 |
| open_access_boolean | |
| owner | DE-739 DE-188 DE-521 DE-824 DE-703 DE-83 |
| owner_facet | DE-739 DE-188 DE-521 DE-824 DE-703 DE-83 |
| physical | XX, 630 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Statistics: textbooks & monographs A Chapman & Hall book |
| spelling | Gibbons, Jean Dickinson 1938- Verfasser (DE-588)132991373 aut Nonparametric statistical inference Jean Dickinson Gibbons ; Subhabrata Chakraborti 5. ed. Boca Raton [u.a.] CRC Press 2011 XX, 630 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics: textbooks & monographs A Chapman & Hall book Includes bibliographical references and index Nonparametric statistics Nichtparametrische Statistik (DE-588)4226777-8 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Inferenzstatistik (DE-588)4247120-5 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Inferenzstatistik (DE-588)4247120-5 s DE-604 Nichtparametrische Statistik (DE-588)4226777-8 s Statistik (DE-588)4056995-0 s 2\p DE-604 Chakraborti, Subhabrata 1957- Verfasser (DE-588)120879131 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020572504&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 | Gibbons, Jean Dickinson 1938- Chakraborti, Subhabrata 1957- Nonparametric statistical inference Nonparametric statistics Nichtparametrische Statistik (DE-588)4226777-8 gnd Statistik (DE-588)4056995-0 gnd Inferenzstatistik (DE-588)4247120-5 gnd |
| subject_GND | (DE-588)4226777-8 (DE-588)4056995-0 (DE-588)4247120-5 (DE-588)4123623-3 |
| title | Nonparametric statistical inference |
| title_auth | Nonparametric statistical inference |
| title_exact_search | Nonparametric statistical inference |
| title_full | Nonparametric statistical inference Jean Dickinson Gibbons ; Subhabrata Chakraborti |
| title_fullStr | Nonparametric statistical inference Jean Dickinson Gibbons ; Subhabrata Chakraborti |
| title_full_unstemmed | Nonparametric statistical inference Jean Dickinson Gibbons ; Subhabrata Chakraborti |
| title_short | Nonparametric statistical inference |
| title_sort | nonparametric statistical inference |
| topic | Nonparametric statistics Nichtparametrische Statistik (DE-588)4226777-8 gnd Statistik (DE-588)4056995-0 gnd Inferenzstatistik (DE-588)4247120-5 gnd |
| topic_facet | Nonparametric statistics Nichtparametrische Statistik Statistik Inferenzstatistik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020572504&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gibbonsjeandickinson nonparametricstatisticalinference AT chakrabortisubhabrata nonparametricstatisticalinference |