Robust nonparametric statistical methods
"Often referred to as distribution-free methods, nonparametric methods do not rely on assumptions that the data are drawn from a given probability distribution. With an emphasis on Wilcoxon rank methods that enable a unified approach to data analysis, this book presents a unique overview of rob...
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
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Boca Raton, Fla. [u.a.]
CRC Press
2011
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| Ausgabe: | 2. ed. |
| Schriftenreihe: | Monographs on statistics and applied probability
119 |
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| 020 | |a 9781439809082 |9 978-1-4398-0908-2 | ||
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| 100 | 1 | |a Hettmansperger, Thomas P. |d 1939- |e Verfasser |0 (DE-588)124200605 |4 aut | |
| 245 | 1 | 0 | |a Robust nonparametric statistical methods |c Thomas P. Hettmansperger ; Joseph W. McKean |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b CRC Press |c 2011 | |
| 300 | |a XVII, 535 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Monographs on statistics and applied probability |v 119 | |
| 500 | |a Includes bibliographical references (p. 495-520) and indexes | ||
| 520 | |a "Often referred to as distribution-free methods, nonparametric methods do not rely on assumptions that the data are drawn from a given probability distribution. With an emphasis on Wilcoxon rank methods that enable a unified approach to data analysis, this book presents a unique overview of robust nonparametric statistical methods. Drawing on examples from various disciplines, the relevant R code for these examples, as well as numerous exercises for self-study, the text covers location models, regression models, designed experiments, and multivariate methods. This edition features a new chapter on cluster correlated data"-- | ||
| 650 | 4 | |a Nonparametric statistics | |
| 650 | 4 | |a Robust statistics | |
| 650 | 7 | |a MATHEMATICS / Probability & Statistics / General |2 bisacsh | |
| 650 | 0 | 7 | |a Robuste Statistik |0 (DE-588)4451047-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtparametrische Statistik |0 (DE-588)4226777-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtparametrische Statistik |0 (DE-588)4226777-8 |D s |
| 689 | 0 | 1 | |a Robuste Statistik |0 (DE-588)4451047-0 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a McKean, Joseph W. |d 1944- |e Verfasser |0 (DE-588)124200540 |4 aut | |
| 830 | 0 | |a Monographs on statistics and applied probability |v 119 |w (DE-604)BV002494005 |9 119 | |
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Datensatz im Suchindex
| _version_ | 1819641255192166400 |
|---|---|
| adam_text | Contents
Preface
xv
1
One-Sample Problems
1
1.1
Introduction
............................ 1
1.2
Location Model
.......................... 2
1.3
Geometry and Inference in the Location Model
......... 5
1.3.1
Computation
....................... 13
1.4
Examples
............................. 14
1.5
Properties of Norm-Based Inference
............... 19
1.5.1
Basic Properties of the Power Function
75(6*) ..... 20
1.5.2
Asymptotic Linearity and Pitman Regularity
...... 22
1.5.3
Asymptotic Theory and Efficiency Results for
θ
. . . . 26
1.5.4
Asymptotic Power and Efficiency Results for the Test
Based on S{0)
....................... 27
1.5.5
Efficiency Results for Confidence Intervals Based on S{6)
29
1.6
Robustness Properties of Norm-Based Inference
........ 32
1.6.1
Robustness Properties of
θ
................ 33
1.6.2
Breakdown Properties of Tests
.............. 35
1.7
Inference and the Wilcoxon Signed-Rank Norm
........ 38
1.7.1
Null Distribution Theory of
Т(0)
............ 39
1.7.2
Statistical Properties
................... 40
1.7.3
Robustness Properties
.................. 46
1.8
Inference Based on General Signed-Rank Norms
........ 48
1.8.1
Null Properties of the Test
................ 50
1.8.2
Efficiency and Robustness Properties
.......... 51
1.9
Ranked Set Sampling
....................... 57
1.10 Lx
Interpolated Confidence Intervals
.............. 61
1.11
Two-Sample Analysis
....................... 65
1.12
Exercises
.............................. 70
x
CONTENTS
2
Two-Sample Problems
77
2.1
Introduction
............................ 77
2.2
Geometric Motivation
...................... 78
2.2.1
Least Squares (LS) Analysis
............... 81
2.2.2
Mann-Whitney-Wilcoxon (MWW) Analysis
...... 82
2.2.3
Computation
....................... 84
2.3
Examples
............................. 84
2.4
Inference Based on the Mann-Whitney-Wilcoxon
........ 87
2.4.1
Testing
........................... 87
2.4.2
Confidence Intervals
................... 97
2.4.3
Statistical Properties of the Inference Based on the MWW
97
2.4.4
Estimation of
Δ
...................... 102
2.4.5
Efficiency Results Based on Confidence Intervals
.... 103
2.5
General Rank Scores
....................... 105
2.5.1
Statistical Methods
.................... 109
2.5.2
Efficiency Results
..................... 110
2.5.3
Connection between One- and Two-Sample Scores
... 113
2.6
L Analyses
............................ 115
2.6.1
Analysis Based on the Lx Pseudo-Norm
......... 115
2.6.2
Analysis Based on the L Norm
............. 119
2.7
Robustness Properties
...................... 122
2.7.1
Breakdown Properties
.................. 122
2.7.2
Influence Functions
.................... 123
2.8
Proportional Hazards
....................... 125
2.8.1
The Log Exponential and the Savage Statistic
..... 126
2.8.2
Efficiency Properties
................... 129
2.9
Two-Sample Rank Set Sampling (RSS)
............. 131
2.10
Two-Sample Scale Problem
................... 133
2.10.1
Appropriate Score Functions
............... 133
2.10.2
Efficacy of the Traditional F-Test
............ 142
2.11
Behrens-Fisher Problem
..................... 144
2.11.1
Behavior of the Usual MWW Test
............ 144
2.11.2
General Rank Tests
.................... 146
2.11.3
Modified Mathisen s Test
................. 147
2.11.4
Modified MWW Test
................... 149
2.11.5
Efficiencies and Discussion
................ 150
2.12
Paired Designs
.......................... 152
2.12.1
Behavior under Alternatives
............... 156
2.13
Exercises
.............................. 157
CONTENTS xi
3 Linear Models 165
3.1
Introduction............................
165
3.2
Geometry
of Estimation and Tests
................ 166
3.2.1
The Geometry of Estimation
............... 166
3.2.2
The Geometry of Testing
................. 169
3.3
Examples
............................. 172
3.4
Assumptions for Asymptotic Theory
.............. 177
3.5
Theory of Rank-Based Estimates
................ 180
3.5.1
R
Estimators of the Regression Coefficients
....... 180
3.5.2
R
Estimates of the Intercept
............... 185
3.6
Theory of Rank-Based Tests
................... 191
3.6.1
Null Theory of Rank-Based Tests
............ 191
3.6.2
Theory of Rank-Based Tests under Alternatives
.... 197
3.6.3
Further Remarks on the Dispersion Function
...... 201
3.7
Implementation of the
R
Analysis
................ 203
3.7.1
Estimates of the Scale Parameter
τψ
.......... 204
3.7.2
Algorithms for Computing the
R
Analysis
....... 207
3.7.3
An Algorithm for a Linear Search
............ 210
3.8
Lx Analysis
............................ 211
3.9
Diagnostics
............................ 213
3.9.1
Properties of
R
Residuals and Model Misspecification
. 214
3.9.2
Standardization of
R
Residuals
............. 220
3.9.3
Measures of Influential Cases
.............. 227
3.10
Survival Analysis
......................... 231
3.11
Correlation Model
......................... 240
3.11.1
Huber s Condition for the Correlation Model
...... 240
3.11.2
Traditional Measure of Association and Its Estimate
. 242
3.11.3
Robust Measure of Association and Its Estimate
.... 243
3.11.4
Properties of
R
Coefficients of Multiple Determination
245
3.11.5
Coefficients of Determination for Regression
...... 250
3.12
High Breakdown (HBR) Estimates
............... 252
3.12.1
Geometry of the HBR Estimates
............ 252
3.12.2
Weights
.........
χ
................ 253
3.12.3
Asymptotic Normality of
ßHBR............. 256
3.12.4
Robustness Properties of the HBR Estimates
...... 260
3.12.5
Discussion
......................... 263
3.12.6
Implementation and Examples
.............. 264
3.12.7
Studentized Residuals
.................. 265
3.12.8
Example on Curvature Detection
............ 267
3.13
Diagnostics for Differentiating between Fits
.......... 268
3.14
Rank-Based Procedures for Nonlinear Models
......... 276
3.14.1
Implementation
...................... 279
xii CONTENTS
3.15
Exercises
.............................. 282
4
Experimental
Designs:
Fixed Effects
291
4.1
Introduction
............................ 291
4.2
One-way Design
.......................... 292
4.2.1
R
Fit of the One-way Design
............... 294
4.2.2
Rank-Based Tests of Ho
:
μλ
= ■ · ■ =
џк........
296
4.2.3
Tests of General Contrasts
................ 299
4.2.4
More on Estimation of Contrasts and Location
..... 300
4.2.5
Pseudo-observations
................... 302
4.3
Multiple Comparison Procedures
................ 304
4.3.1
Discussion
......................... 311
4.4
Two-way Crossed Factorial
.................... 313
4.5
Analysis of Covariance
...................... 317
4.6
Further Examples
......................... 321
4.7
Rank Transform
.......................... 325
4.7.1
Monte Carlo Study
.................... 327
4.8
Exercises
.............................. 331
5
Models with Dependent Error Structure
337
5.1
Introduction
............................ 337
5.2
General Mixed Models
...................... 337
5.2.1
Applications
........................ 342
5.3
Simple Mixed Models
....................... 342
5.3.1
Variance Component Estimators
............. 343
5.3.2
Studentized Residuals
.................. 344
5.3.3
Example and Simulation Studies
............ 346
5.3.4
Simulation Studies of Validity
.............. 347
5.3.5
Simulation Study of Other Score Functions
....... 349
5.4
Arnold Transformations
..................... 350
5.4.1
R
Fit Based on Arnold Transformed Data
....... 351
5.5
General Estimating Equations (GEE)
.............. 356
5.5.1
Asymptotic Theory
.................... 359
5.5.2
Implementation and a Monte Carlo Study
....... 360
5.5.3
Example: Inflammatory Markers
............. 362
5.6
Time Series
............................ 366
5.6.1
Asymptotic Theory
.................... 368
5.6.2 Wald
-Туре
Inference
................... 370
5.6.3
Linear Models with
Autoregressive
Errors
....... 372
5.7
Exercises
.............................. 375
CONTENTS xiii
6 Multivariate 377
6.1 Multivariate
Location
Model................... 377
6.2
Componentwise Methods.....................
382
6.2.1
Estimation
......................... 385
6.2.2
Testing
........................... 386
6.2.3
Componentwise Rank Methods
............. 390
6.3
Spatial Methods
.......................... 392
6.3.1
Spatial Sign Methods
................... 392
6.3.2
Spatial Rank Methods
.................. 399
6.4 Affine Equivariant
and Invariant Methods
........... 403
6.4.1
Blumen s Bivariate Sign Test
.............. 403
6.4.2 Affine
Invariant Sign Tests
................ 405
6.4.3
The Oja Criterion Function
............... 413
6.4.4
Additional Remarks
................... 418
6.5
Robustness of Estimates of Location
.............. 419
6.5.1
Location and Scale
Invariance:
Componentwise Methods
419
6.5.2
Rotation
Invariance:
Spatial Methods
.......... 420
6.5.3
The Spatial Hodges-
Lehmann
Estimate
......... 421
6.5.4 Affine
Equivariant Spatial Median
............ 421
6.5.5 Affine
Equivariant Oja Median
............. 422
6.6
Linear Model
........................... 422
6.6.1
Test for Regression Effect
................ 425
6.6.2
The Estimate of the Regression Effect
......... 431
6.6.3
Tests of General Hypotheses
............... 432
6.7
Experimental Designs
....................... 439
6.8
Exercises
.............................. 443
A Asymptotic Results
447
A.I Central Limit Theorems
..................... 447
A.
2
Simple Linear Rank Statistics
.................. 448
A.
2.1
Null Asymptotic Distribution Theory
.......... 449
A.
2.2
Local Asymptotic Distribution Theory
......... 450
A.2.3 Signed-Rank Statistics
.................. 457
A.3 Rank-Based Analysis of Linear Models
............. 460
A.
3.1
Convex Functions
..................... 463
A.
3.2
Asymptotic Linearity and Quadraticity
......... 464
A.
3.3
Asymptotic Distance between
β
and
β
......... 467
A.
3.4
Consistency of the Test Statistic Fv
........... 468
A.3.5 Proof of Lemma
3.5.1................... 469
A.
4
Asymptotic Linearity for the L Analysis
............ 470
A.
5
Influence Functions
........................ 473
xiv CONTENTS
Α.
5.1
Influence
Function for Estimates Based on Signed-Rank
Statistics
.......................... 474
A.
5.2
Influence Functions for Chapter
3............ 476
A.5.3 Influence Function of
ßHBR
of Section
3.12.4...... 482
A.6 Asymptotic Theory for Section
3.12.3.............. 484
A.7 Asymptotic Theory for Section
3.12.7.............. 491
A.
8
Asymptotic Theory for Section
3.13............... 492
References
495
Author Index
521
Index
527
Statistics
Presenting an extensive set of tools and methods for data analysis, Robust
Nonparametric Statistical Methods, Second Edition covers univariate
tests and estimates with extensions to linear models, multivariate models,
times series models, experimental designs, and mixed models. It follows
the approach of the first edition by developing rank-based methods from
the unifying theme of geometry. This edition, however, includes more mod¬
els and methods and significantly extends the possible analyses based on
ranks.
New to the Second Edition
•
A new section on rank procedures for nonlinear models
•
A new chapter on models with dependent error structure, covering
rank methods for mixed models, general estimating equations, and
time series
•
New material on the development of computationally efficient
affine
invariant/equivariant sign methods based on transform-retransform
techniques in multivariate models
Taking a comprehensive, unified approach to statistical analysis, the book
continues to describe one- and two-sample problems, the basic develop¬
ment of rank methods in the linear model, and fixed effects experimental
designs. It also explores models with dependent error structure and mul¬
tivariate models. The authors illustrate the implementation of the methods
using many real-world examples and R. More information about the data
sets and
R
packages can be found at www.crcpress.com.
|
| any_adam_object | 1 |
| author | Hettmansperger, Thomas P. 1939- McKean, Joseph W. 1944- |
| author_GND | (DE-588)124200605 (DE-588)124200540 |
| author_facet | Hettmansperger, Thomas P. 1939- McKean, Joseph W. 1944- |
| author_role | aut aut |
| author_sort | Hettmansperger, Thomas P. 1939- |
| author_variant | t p h tp tph j w m jw jwm |
| building | Verbundindex |
| bvnumber | BV037384290 |
| classification_rvk | QH 233 SK 830 SK 835 SK 840 |
| ctrlnum | (OCoLC)645676599 (DE-599)BVBBV037384290 |
| 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 |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV037384290 |
| illustrated | Illustrated |
| indexdate | 2024-12-24T01:01:14Z |
| institution | BVB |
| isbn | 9781439809082 1439809089 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022537356 |
| oclc_num | 645676599 |
| open_access_boolean | |
| owner | DE-521 DE-824 DE-M382 DE-739 DE-83 DE-188 DE-N2 |
| owner_facet | DE-521 DE-824 DE-M382 DE-739 DE-83 DE-188 DE-N2 |
| physical | XVII, 535 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | CRC Press |
| record_format | marc |
| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spellingShingle | Hettmansperger, Thomas P. 1939- McKean, Joseph W. 1944- Robust nonparametric statistical methods Monographs on statistics and applied probability Nonparametric statistics Robust statistics MATHEMATICS / Probability & Statistics / General bisacsh Robuste Statistik (DE-588)4451047-0 gnd Nichtparametrische Statistik (DE-588)4226777-8 gnd |
| subject_GND | (DE-588)4451047-0 (DE-588)4226777-8 |
| title | Robust nonparametric statistical methods |
| title_auth | Robust nonparametric statistical methods |
| title_exact_search | Robust nonparametric statistical methods |
| title_full | Robust nonparametric statistical methods Thomas P. Hettmansperger ; Joseph W. McKean |
| title_fullStr | Robust nonparametric statistical methods Thomas P. Hettmansperger ; Joseph W. McKean |
| title_full_unstemmed | Robust nonparametric statistical methods Thomas P. Hettmansperger ; Joseph W. McKean |
| title_short | Robust nonparametric statistical methods |
| title_sort | robust nonparametric statistical methods |
| topic | Nonparametric statistics Robust statistics MATHEMATICS / Probability & Statistics / General bisacsh Robuste Statistik (DE-588)4451047-0 gnd Nichtparametrische Statistik (DE-588)4226777-8 gnd |
| topic_facet | Nonparametric statistics Robust statistics MATHEMATICS / Probability & Statistics / General Robuste Statistik Nichtparametrische Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022537356&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022537356&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002494005 |
| work_keys_str_mv | AT hettmanspergerthomasp robustnonparametricstatisticalmethods AT mckeanjosephw robustnonparametricstatisticalmethods |