An introduction to modern nonparametric statistics:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Pacific Grove, CA
Thomson ; Brooks/Cole
2004
|
| Series: | Duxbury advanced series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 351-355) and index |
| Physical Description: | XVIII, 366 S. graph. Darst. |
| ISBN: | 0534387756 |
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MARC
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| 100 | 1 | |a Higgins, James J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to modern nonparametric statistics |c James J. Higgins |
| 264 | 1 | |a Pacific Grove, CA |b Thomson ; Brooks/Cole |c 2004 | |
| 300 | |a XVIII, 366 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Duxbury advanced series | |
| 500 | |a Includes bibliographical references (p. 351-355) and index | ||
| 650 | 7 | |a Non-parametrische statistiek |2 gtt | |
| 650 | 4 | |a Nonparametric statistics | |
| 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 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016766056&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016766056 | ||
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| _version_ | 1804138058763730944 |
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| adam_text | Contents
в
Preliminaries
1
0.1
Cumulative Distributions and Probability Density Functions
1
0.2
Common Continuous Probability Distributions
1
0.3
The Binomial Distribution
4
0.4
Confidence Intervals and Tests of Hypotheses
5
0.5
Parametric versus Nonparametric Methods
7
0.6
Classes of Nonparametric Methods
7
One-Sample Methods
11
1.1
A Nonparametric Test of Hypothesis and
Confidence Interval for the Median 1
1
1.1.1
Binomial Test
11
1.1.2
Confidence Interval
13
1.1.3
Computer Analysis
14
1.2
Estimating the Population cdf and Percentiles
14
1.2.1
Confidence Interval for the Population cdf
14
1.2.2
Inferences for Percentiles
16
1.2.3
Computer Analysis
17
13
A Comparison of Statistical Tests
17
1.3.1
Type I Errors
18
1.3.2
Power
18
1.3.3
Derivations
20
Exercises
21
VÍ
Contents
ì
Two-Sample Methods
23
2.1
A Two-Sample Permutation Test
23
2.1.1
The Permutation Test
24
2.1.2
Summary of Steps Used in a Two-Sample Permutation Test
27
2.1.3
Hypotheses for the Two-Sample Permutation Test
28
2.1.4
Computer Analysis
29
2.2
Permutation Tests Based on the Median and Trimmed Means
30
2.2.1
A Permutation Test Based on Medians
30
2.2.2
Trimmed Means
31
2.3
Random Sampling the Permutations
31
2.3.1
An Approximate p-Value Based on
Random Sampling the Permutations
32
2.3.2
Computer Analysis Using Resampling Stats
33
2.3.3
Computer Analysis Using StatXact
35
2.4
Wilcoxon Rank-Sum Test
35
2.4.1
Steps in Conducting the Wilcoxon Rank-Sum Test
37
2.4.2
Comments on the Use of the Wilcoxon Rank-Sum Test
38
2.4.3
A Statistical Table for the Wilcoxon Rank-Sum Test
38
2.4.4
Computer Analysis
39
2.5
Wilcoxon Rank-Sum Test Adjusted for Ties
41
2.5.1
Steps in Conducting the Wilcoxon Rank-Sum Test
Adjusted for Ties
41
2.5.2
Computer Analysis
42
2.6
Mann-Whitney Test and a Confidence Interval
43
2.6.1
The Mann-Whitney Statistic
43
2.6.2
Equivalence of Mann-Whitney and
Wilcoxon Rank-Sum Statistics
44
2.6.3
A Confidence Interval for a Shift Parameter
and the Hodges—
Lehmann
Estimate
45
2.6.4
Computer Analysis
48
2.7
Scoring Systems
49
2.7.1
Three Common Scoring Systems
49
2.7.2
Computer Analysis
51
2.8
Tests for Equality of Scale Parameters and an Omnibus Test
51
2.8.1
Siegel-Tukey and Ansari-Bradley Test
52
2.8.2
Tests on
Déviances
53
2.8.3
Kolmogorov-Smirnov Test
57
2.8.4
Computer Analysis
58
Contents
ЇІІ
2.9
Selecting Among Two-Sample
Tests 58
2.9.1
The
ŕ-Test
60
2.9.2
The Wilcoxon Rank-Sum Test versus the f-Test
61
2.9.3
Relative Efficiency
62
2.9.4
Power of Permutation Tests
63
2.10
Large-Sample Approximations
65
2.10.1
Sampling Formulas
65
2.10.2
Application to the Wilcoxon Rank-Sum Test
66
2.10.3
Wilcoxon Rank-Sum Test with Ties
68
2.10.4
Explicit Formulas for
£(
W^) and var(
WÜJ 70
2.10.5
Large-Sample Confidence Interval Based
on Mann-Whitney Test
71
2.10.6
A Normal Approximation for the Permutation Distribution
72
Exercises
73
3
^-Sample Methods
79
3.1
^-Sample Permutation Tests
79
3.1.1
The
F
Statistic
80
3.1.2
Steps in Carrying Out the Permutation F-Test
81
3.1.3
Alternative Forms of the Permutation
F
Statistic
83
3.1.4
Computer Analysis
84
3.2
The Kruskal-Wallis Test
86
3.2.1
The Kruskal-Wallis Statistic
86
3.2.2
Adjustment for Ties
88
3.2.3
An Intuitive Derivation of the Chi-Square
Approximation for KW
90
3.2.4
Tests on General Scores
91
3.2.5
Computer Analysis
91
3
J
Multiple Comparisons
92
3.3.1
Three Rank-Based Procedures for Controlling Experiment-Wise
Error Rate Assuming No Ties in the Data
92
3.3.2
Multiple Comparisons for General Scores (Including Ties)
96
3.3.3
Multiple Comparison Permutation Tests
96
3.3.4
Variance of a Difference of Means When Sampling
from a Finite Population
98
3.3.5
Computer Analysis
99
3.4
Ordered Alternatives
99
Contents
4
3.4.1 Jonckheere-TerpstraTest 101
3.4.2
Large-Sample
Approximation 101
3.4.3 Computer
Analysis
103
Exercises
105
Paired Comparisons and Blocked Designs
109
4.1
Paired-Comparison Permutation Test
109
4.1.1
Steps for a Paired-Comparison Permutation Test
110
4.1.2
Randomly Selected Permutations
113
4.1.3
Large-Sample Approximations
113
4.1.4
A Test for the Median of a Symmetric Population
114
4.1.5
Computer Analysis
114
4.2
Signed-Rank Test
117
4.2.1
The Wilcoxon Signed-Rank Test without Ties in the Data
118
4.2.2
Large-Sample Approximation
118
4.2.3
Adjustment for Ties
120
4.2.4
Computer Analysis
124
4.3
Other Paired-Comparison Tests
125
4.3.1
Sign Test
125
4.3.2
General Scoring Systems
126
4.3.3
Selecting Among Paired-Comparison Tests
127
4.4
A Permutation Test for a Randomized Complete Block Design
127
4.4.1
F
Statistic for Randomized Complete Block Designs
128
4.4.2
Permutation F-Test for Randomized Complete Block Designs
129
4.4.3
Multiple Comparisons
130
4.4.4
Computer Analysis
131
4.5
Friedman s Test for a Randomized Complete Block Design
132
4.5.1
Friedman s Test without Ties
133
4.5.2
Adjustment for Ties
134
4.5.3
Cochran s
β
and Kendall s
W
136
4.5.4
Chi-Square Approximation for
FM
or FMjjjs
136
4.5.5
Computer Analysis
137
4.6
Ordered Alternatives for a Randomized Complete Block Design
138
4.6.1
Page s Test
139
4.6.2
Computer Analysis
140
Exercises
141
5
Contents
IX
Tests for Trends and Association
145
5.1
A Permutation Test for Correlation and Slope
145
5.1.1
The Correlation Coefficient
145
5.1.2
Slope of Least Squares Line
146
5.1.3
The Permutation Test
147
5.1.4
Large-Sample Approximation for the
Permutation Distribution of
r
151
5.1.5
Computer Analysis
152
5.2
Spearman Rank Correlation
153
5.2.1
Statistical Test for Spearman Rank Correlation
154
5.2.2
Large-Sample Approximation
154
5.2.3
Computer Analysis
158
5.3
Kendall s
Tau 158
5.3.1
Estimating Kendall s
Tau
with No Ties in the Data
159
5.3.2
Large-Sample Approximation
160
5.3.3
Adjustment for Ties in the Data
161
5.3.4
Computer Analysis
163
5.4
Permutation Tests for Contingency Tables
163
5.4.1
Hypotheses to Be Tested and the Chi-Square Statistic
163
5.4.2
Permutation Chi-Square Test
165
5.4.3
Multiple Comparisons in Contingency Tables
167
5.4.4
Computer Analysis
169
5.5
Fisher s Exact Test for a
2
x
2
Contingency Table
172
5.5.1
Probability Distribution Under the Null Hypothesis
173
5.5.2
Computer Analysis
175
5.6
Contingency Tables with Ordered Categories
176
5.6.1
Singly Ordered Tables
176
5.6.2
Doubly Ordered Tables
178
5.6.3
Computer Analysis
179
5.7
Mantel-HaenszelTest
179
5.7.1
Hypotheses to Be Tested
179
5.7.2
Testing Hypotheses for Stratified Contingency Tables
181
5.7.3
Estimation of the Odds Ratio
183
5.7.4
Computer Analysis
184
5.8
McNemar sTest
186
5.8.1
Notation and Hypotheses
187
5.8.2
Test Statistic and Permutation Distribution
187
5.8.3
Computer Analysis
188
Exercises
189
І
Contents
в
7
Multivariate Tests 195
6.1
Two-Sample
Multivariate
Permutation
Tests 195
6.1.1 Notation
and Assumptions
196
6.1.2
The Permutation Version of Hotelling s T2
197
6.1.3
Other Multivariate Statistics
198
6.1.4
Computer Analysis
200
6.2
Two-Sample Multivariate Rank Tests
202
6.2.1
A Sum of Wilcoxon Statistics
203
6.2.2
Computer Analysis
205
6.3
Multivariate Paired Comparisons
206
6.3.1
A Permutation Test Based on T2
207
6.3.2
Random Sampling the Permutations
207
6.3.3
Other Multivariate Statistics
209
6.3.4
Computer Analysis
210
6.4
Multivariate Rank Tests for Paired Comparisons
210
6.4.1
Testing Medians of a Symmetric Distribution
212
6.4.2
A Sum of Signed-Rank Statistics
214
6.4.3
Computer Analysis
216
6.5
Multiresponse Categorical Data
216
6.5.1
Hypotheses for Multiresponse Data
217
6.5.2
A Statistical Test
218
6.5.3
Computer Analysis
220
Exercises
222
Analysis of Censored Data
225
7.1
Estimating the Survival Function
225
7.1.1
Censored Data
225
7.1.2
Kaplan-Meier Estimate
226
7.1.3
Computer Analysis
228
7.2
Permutation Tests for Two-Sample Censored Data
229
7.2.1
Censoring Mechanism
229
7.2.2
Examples of Tests Based on Medians and Ranks
231
7.2.3
Computer Analysis
232
7.3
Gehan s Generalization of the Mann-Whitney Test
232
7.3.1
An Alternative Form of Oc Based on Gehan Scores
233
7.3.2
Large-Sample Approximations
235
7.3.3
Computer Analysis
236
8
Contents XI
7.4
Scoring Systems for Censored Data
236
7.4.1
Prentice-Wilcoxon Scores
236
7.4.2
Log-Rank Scores
238
7.4.3
The Likelihood Approach
239
7.4.4
Computer Analysis
241
7.5
Tests Using Scoring Systems for Censored Data
242
7.5.1
Two-Sample and AT-Sample Tests
242
7.5.2
Paired-Comparison and Blocked Designs
244
7.5.3
Computer Analysis
245
Exercises
245
Nonparametric Bootstrap Methods
249
8.1
The Basic Bootstrap Method
249
8.1.1
Mean Squared Error and Margin of Error
250
8
Л
.2
The Bootstrap Estimate of
MSE
250
8.1.3
Computer Analysis
253
8.2
Bootstrap Intervals for Location-Scale Models
254
8.2.1
Interval Estimate of the Mean
255
8.2.2
Confidence Intervals for the Variance
and Standard Deviation
257
8.2.3
Coverage Percentages
258
8.2.4
Derivation of Pivotal Quantities
259
8.2.5
Computer Analysis
260
83
ВС
A and Other Bootstrap Intervals
26
1
8.3.1
Percentile and Residual Methods
261
8.3.2
BCA Method
262
8.3.3
Computer Analysis
265
8.4
Correlation and Regression
266
8.4.1
Bivariate Bootstrap Sampling
266
8.4.2
Fixed-X Bootstrap Sampling
268
8.4.3
Bootstrap Inferences for the Slope of a Regression Line
270
8.4.4
Computer Analysis
274
8.5
Two-Sample Inference
276
8.5.1
f-Pivot Method Assuming Equality of Error Distributions
276
8.5.2
Unequal Distributions of the Errors
278
8.5.3
Computer Analysis
281
8.6
Bootstrap Sampling from Several Populations
283
8.6.1
Equal Error Distributions
283
XU Contents
8.6.2
Unequal Error Distributions
285
8.6.3
Regression with Unequal Error Variances
285
8.6.4
Computer Analysis
288
8.7
Bootstrap Sampling for Multiple Regression
288
8.7.1
The Bootstrap Procedure for Testing H^ and
Нщ
289
8.7.2
A Confidence Interval for pV
290
8.7.3
Theoretical Development
292
8.7.4
Other Methods for Regression Analysis
295
8.7.5
Computer Analysis
296
Exercises
298
Я
Multifactor Experiments
301
9.1
Analysis of Variance Models
301
9.1.1
The Bootstrap Approach to the Analysis
of the Fixed-Effects Model
302
9.1.2
A Permutation Test for the Overall Effect of a Factor
305
9.1.3
Computer Analysis
307
9.2
Aligned-Rank Transform
309
9.2.1
Aligning the Data in a Completely Random Design
310
9.2.2
Aligning the Data in a Split-Plot Design
311
9.2.3
Properties of the Aligned-Rank Procedure
314
9.2.4
Computer Analysis
314
93
Testing for Lattice-Ordered Alternatives
314
9.3.1
A Test Statistic for Lattice-Ordered Alternatives
315
9.3.2
Lattice Correlation
316
9.3.3
References for Lattice-Ordered Alternatives
318
9.3.4
Computer Analysis
319
Exercises
319
10
Smoothing Methods and Robust Model Fitting
323
10.1
Estimating the Probability Density Function
323
10.1.1
Kernel Method
324
10.1.2
Computer Analysis
326
10.2
Nonparametric Curve Smoothing
326
10.2.1
Loess Method
326
10.2.2
Kernel Method
327
10.2.3
Computer Analysis
329
Contents
ХНІ
103 Robust
and Rank-Based
Regression 329
10.3.1 M-Estimation 329
10.3.2
Rank-Based
Regression 331
10.3.3 Computer
Analysis
334
Exercises
334
Appendix
337
References
351
Index
356
|
| adam_txt |
Contents
в
Preliminaries
1
0.1
Cumulative Distributions and Probability Density Functions
1
0.2
Common Continuous Probability Distributions
1
0.3
The Binomial Distribution
4
0.4
Confidence Intervals and Tests of Hypotheses
5
0.5
Parametric versus Nonparametric Methods
7
0.6
Classes of Nonparametric Methods
7
One-Sample Methods
11
1.1
A Nonparametric Test of Hypothesis and
Confidence Interval for the Median 1
1
1.1.1
Binomial Test
11
1.1.2
Confidence Interval
13
1.1.3
Computer Analysis
14
1.2
Estimating the Population cdf and Percentiles
14
1.2.1
Confidence Interval for the Population cdf
14
1.2.2
Inferences for Percentiles
16
1.2.3
Computer Analysis
17
13
A Comparison of Statistical Tests
17
1.3.1
Type I Errors
18
1.3.2
Power
18
1.3.3
Derivations
20
Exercises
21
VÍ
Contents
ì
Two-Sample Methods
23
2.1
A Two-Sample Permutation Test
23
2.1.1
The Permutation Test
24
2.1.2
Summary of Steps Used in a Two-Sample Permutation Test
27
2.1.3
Hypotheses for the Two-Sample Permutation Test
28
2.1.4
Computer Analysis
29
2.2
Permutation Tests Based on the Median and Trimmed Means
30
2.2.1
A Permutation Test Based on Medians
30
2.2.2
Trimmed Means
31
2.3
Random Sampling the Permutations
31
2.3.1
An Approximate p-Value Based on
Random Sampling the Permutations
32
2.3.2
Computer Analysis Using Resampling Stats
33
2.3.3
Computer Analysis Using StatXact
35
2.4
Wilcoxon Rank-Sum Test
35
2.4.1
Steps in Conducting the Wilcoxon Rank-Sum Test
37
2.4.2
Comments on the Use of the Wilcoxon Rank-Sum Test
38
2.4.3
A Statistical Table for the Wilcoxon Rank-Sum Test
38
2.4.4
Computer Analysis
39
2.5
Wilcoxon Rank-Sum Test Adjusted for Ties
41
2.5.1
Steps in Conducting the Wilcoxon Rank-Sum Test
Adjusted for Ties
41
2.5.2
Computer Analysis
42
2.6
Mann-Whitney Test and a Confidence Interval
43
2.6.1
The Mann-Whitney Statistic
43
2.6.2
Equivalence of Mann-Whitney and
Wilcoxon Rank-Sum Statistics
44
2.6.3
A Confidence Interval for a Shift Parameter
and the Hodges—
Lehmann
Estimate
45
2.6.4
Computer Analysis
48
2.7
Scoring Systems
49
2.7.1
Three Common Scoring Systems
49
2.7.2
Computer Analysis
51
2.8
Tests for Equality of Scale Parameters and an Omnibus Test
51
2.8.1
Siegel-Tukey and Ansari-Bradley Test
52
2.8.2
Tests on
Déviances
53
2.8.3
Kolmogorov-Smirnov Test
57
2.8.4
Computer Analysis
58
Contents
ЇІІ
2.9
Selecting Among Two-Sample
Tests 58
2.9.1
The
ŕ-Test
60
2.9.2
The Wilcoxon Rank-Sum Test versus the f-Test
61
2.9.3
Relative Efficiency
62
2.9.4
Power of Permutation Tests
63
2.10
Large-Sample Approximations
65
2.10.1
Sampling Formulas
65
2.10.2
Application to the Wilcoxon Rank-Sum Test
66
2.10.3
Wilcoxon Rank-Sum Test with Ties
68
2.10.4
Explicit Formulas for
£(
W^) and var(
WÜJ 70
2.10.5
Large-Sample Confidence Interval Based
on Mann-Whitney Test
71
2.10.6
A Normal Approximation for the Permutation Distribution
72
Exercises
73
3
^-Sample Methods
79
3.1
^-Sample Permutation Tests
79
3.1.1
The
F
Statistic
80
3.1.2
Steps in Carrying Out the Permutation F-Test
81
3.1.3
Alternative Forms of the Permutation
F
Statistic
83
3.1.4
Computer Analysis
84
3.2
The Kruskal-Wallis Test
86
3.2.1
The Kruskal-Wallis Statistic
86
3.2.2
Adjustment for Ties
88
3.2.3
An Intuitive Derivation of the Chi-Square
Approximation for KW
90
3.2.4
Tests on General Scores
91
3.2.5
Computer Analysis
91
3
J
Multiple Comparisons
92
3.3.1
Three Rank-Based Procedures for Controlling Experiment-Wise
Error Rate Assuming No Ties in the Data
92
3.3.2
Multiple Comparisons for General Scores (Including Ties)
96
3.3.3
Multiple Comparison Permutation Tests
96
3.3.4
Variance of a Difference of Means When Sampling
from a Finite Population
98
3.3.5
Computer Analysis
99
3.4
Ordered Alternatives
99
Contents
4
3.4.1 Jonckheere-TerpstraTest 101
3.4.2
Large-Sample
Approximation 101
3.4.3 Computer
Analysis
103
Exercises
105
Paired Comparisons and Blocked Designs
109
4.1
Paired-Comparison Permutation Test
109
4.1.1
Steps for a Paired-Comparison Permutation Test
110
4.1.2
Randomly Selected Permutations
113
4.1.3
Large-Sample Approximations
113
4.1.4
A Test for the Median of a Symmetric Population
114
4.1.5
Computer Analysis
114
4.2
Signed-Rank Test
117
4.2.1
The Wilcoxon Signed-Rank Test without Ties in the Data
118
4.2.2
Large-Sample Approximation
118
4.2.3
Adjustment for Ties
120
4.2.4
Computer Analysis
124
4.3
Other Paired-Comparison Tests
125
4.3.1
Sign Test
125
4.3.2
General Scoring Systems
126
4.3.3
Selecting Among Paired-Comparison Tests
127
4.4
A Permutation Test for a Randomized Complete Block Design
127
4.4.1
F
Statistic for Randomized Complete Block Designs
128
4.4.2
Permutation F-Test for Randomized Complete Block Designs
129
4.4.3
Multiple Comparisons
130
4.4.4
Computer Analysis
131
4.5
Friedman's Test for a Randomized Complete Block Design
132
4.5.1
Friedman's Test without Ties
133
4.5.2
Adjustment for Ties
134
4.5.3
Cochran's
β
and Kendall's
W
136
4.5.4
Chi-Square Approximation for
FM
or FMjjjs
136
4.5.5
Computer Analysis
137
4.6
Ordered Alternatives for a Randomized Complete Block Design
138
4.6.1
Page's Test
139
4.6.2
Computer Analysis
140
Exercises
141
5
Contents
IX
Tests for Trends and Association
145
5.1
A Permutation Test for Correlation and Slope
145
5.1.1
The Correlation Coefficient
145
5.1.2
Slope of Least Squares Line
146
5.1.3
The Permutation Test
147
5.1.4
Large-Sample Approximation for the
Permutation Distribution of
r
151
5.1.5
Computer Analysis
152
5.2
Spearman Rank Correlation
153
5.2.1
Statistical Test for Spearman Rank Correlation
154
5.2.2
Large-Sample Approximation
154
5.2.3
Computer Analysis
158
5.3
Kendall's
Tau 158
5.3.1
Estimating Kendall's
Tau
with No Ties in the Data
159
5.3.2
Large-Sample Approximation
160
5.3.3
Adjustment for Ties in the Data
161
5.3.4
Computer Analysis
163
5.4
Permutation Tests for Contingency Tables
163
5.4.1
Hypotheses to Be Tested and the Chi-Square Statistic
163
5.4.2
Permutation Chi-Square Test
165
5.4.3
Multiple Comparisons in Contingency Tables
167
5.4.4
Computer Analysis
169
5.5
Fisher's Exact Test for a
2
x
2
Contingency Table
172
5.5.1
Probability Distribution Under the Null Hypothesis
173
5.5.2
Computer Analysis
175
5.6
Contingency Tables with Ordered Categories
176
5.6.1
Singly Ordered Tables
176
5.6.2
Doubly Ordered Tables
178
5.6.3
Computer Analysis
179
5.7
Mantel-HaenszelTest
179
5.7.1
Hypotheses to Be Tested
179
5.7.2
Testing Hypotheses for Stratified Contingency Tables
181
5.7.3
Estimation of the Odds Ratio
183
5.7.4
Computer Analysis
184
5.8
McNemar'sTest
186
5.8.1
Notation and Hypotheses
187
5.8.2
Test Statistic and Permutation Distribution
187
5.8.3
Computer Analysis
188
Exercises
189
І
Contents
в
7
Multivariate Tests 195
6.1
Two-Sample
Multivariate
Permutation
Tests 195
6.1.1 Notation
and Assumptions
196
6.1.2
The Permutation Version of Hotelling's T2
197
6.1.3
Other Multivariate Statistics
198
6.1.4
Computer Analysis
200
6.2
Two-Sample Multivariate Rank Tests
202
6.2.1
A Sum of Wilcoxon Statistics
203
6.2.2
Computer Analysis
205
6.3
Multivariate Paired Comparisons
206
6.3.1
A Permutation Test Based on T2
207
6.3.2
Random Sampling the Permutations
207
6.3.3
Other Multivariate Statistics
209
6.3.4
Computer Analysis
210
6.4
Multivariate Rank Tests for Paired Comparisons
210
6.4.1
Testing Medians of a Symmetric Distribution
212
6.4.2
A Sum of Signed-Rank Statistics
214
6.4.3
Computer Analysis
216
6.5
Multiresponse Categorical Data
216
6.5.1
Hypotheses for Multiresponse Data
217
6.5.2
A Statistical Test
218
6.5.3
Computer Analysis
220
Exercises
222
Analysis of Censored Data
225
7.1
Estimating the Survival Function
225
7.1.1
Censored Data
225
7.1.2
Kaplan-Meier Estimate
226
7.1.3
Computer Analysis
228
7.2
Permutation Tests for Two-Sample Censored Data
229
7.2.1
Censoring Mechanism
229
7.2.2
Examples of Tests Based on Medians and Ranks
231
7.2.3
Computer Analysis
232
7.3
Gehan's Generalization of the Mann-Whitney Test
232
7.3.1
An Alternative Form of Oc Based on Gehan Scores
233
7.3.2
Large-Sample Approximations
235
7.3.3
Computer Analysis
236
8
Contents XI
7.4
Scoring Systems for Censored Data
236
7.4.1
Prentice-Wilcoxon Scores
236
7.4.2
Log-Rank Scores
238
7.4.3
The Likelihood Approach
239
7.4.4
Computer Analysis
241
7.5
Tests Using Scoring Systems for Censored Data
242
7.5.1
Two-Sample and AT-Sample Tests
242
7.5.2
Paired-Comparison and Blocked Designs
244
7.5.3
Computer Analysis
245
Exercises
245
Nonparametric Bootstrap Methods
249
8.1
The Basic Bootstrap Method
249
8.1.1
Mean Squared Error and Margin of Error
250
8
Л
.2
The Bootstrap Estimate of
MSE
250
8.1.3
Computer Analysis
253
8.2
Bootstrap Intervals for Location-Scale Models
254
8.2.1
Interval Estimate of the Mean
255
8.2.2
Confidence Intervals for the Variance
and Standard Deviation
257
8.2.3
Coverage Percentages
258
8.2.4
Derivation of Pivotal Quantities
259
8.2.5
Computer Analysis
260
83
ВС
A and Other Bootstrap Intervals
26
1
8.3.1
Percentile and Residual Methods
261
8.3.2
BCA Method
262
8.3.3
Computer Analysis
265
8.4
Correlation and Regression
266
8.4.1
Bivariate Bootstrap Sampling
266
8.4.2
Fixed-X Bootstrap Sampling
268
8.4.3
Bootstrap Inferences for the Slope of a Regression Line
270
8.4.4
Computer Analysis
274
8.5
Two-Sample Inference
276
8.5.1
f-Pivot Method Assuming Equality of Error Distributions
276
8.5.2
Unequal Distributions of the Errors
278
8.5.3
Computer Analysis
281
8.6
Bootstrap Sampling from Several Populations
283
8.6.1
Equal Error Distributions
283
XU Contents
8.6.2
Unequal Error Distributions
285
8.6.3
Regression with Unequal Error Variances
285
8.6.4
Computer Analysis
288
8.7
Bootstrap Sampling for Multiple Regression
288
8.7.1
The Bootstrap Procedure for Testing H^ and
Нщ
289
8.7.2
A Confidence Interval for pV
290
8.7.3
Theoretical Development
292
8.7.4
Other Methods for Regression Analysis
295
8.7.5
Computer Analysis
296
Exercises
298
Я
Multifactor Experiments
301
9.1
Analysis of Variance Models
301
9.1.1
The Bootstrap Approach to the Analysis
of the Fixed-Effects Model
302
9.1.2
A Permutation Test for the Overall Effect of a Factor
305
9.1.3
Computer Analysis
307
9.2
Aligned-Rank Transform
309
9.2.1
Aligning the Data in a Completely Random Design
310
9.2.2
Aligning the Data in a Split-Plot Design
311
9.2.3
Properties of the Aligned-Rank Procedure
314
9.2.4
Computer Analysis
314
93
Testing for Lattice-Ordered Alternatives
314
9.3.1
A Test Statistic for Lattice-Ordered Alternatives
315
9.3.2
Lattice Correlation
316
9.3.3
References for Lattice-Ordered Alternatives
318
9.3.4
Computer Analysis
319
Exercises
319
10
Smoothing Methods and Robust Model Fitting
323
10.1
Estimating the Probability Density Function
323
10.1.1
Kernel Method
324
10.1.2
Computer Analysis
326
10.2
Nonparametric Curve Smoothing
326
10.2.1
Loess Method
326
10.2.2
Kernel Method
327
10.2.3
Computer Analysis
329
Contents
ХНІ
103 Robust
and Rank-Based
Regression 329
10.3.1 M-Estimation 329
10.3.2
Rank-Based
Regression 331
10.3.3 Computer
Analysis
334
Exercises
334
Appendix
337
References
351
Index
356 |
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| index_date | 2024-07-02T22:13:07Z |
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| institution | BVB |
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| language | English |
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| spelling | Higgins, James J. Verfasser aut An introduction to modern nonparametric statistics James J. Higgins Pacific Grove, CA Thomson ; Brooks/Cole 2004 XVIII, 366 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Duxbury advanced series Includes bibliographical references (p. 351-355) and index Non-parametrische statistiek gtt Nonparametric statistics Nichtparametrische Statistik (DE-588)4226777-8 gnd rswk-swf Nichtparametrische Statistik (DE-588)4226777-8 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016766056&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Higgins, James J. An introduction to modern nonparametric statistics Non-parametrische statistiek gtt Nonparametric statistics Nichtparametrische Statistik (DE-588)4226777-8 gnd |
| subject_GND | (DE-588)4226777-8 |
| title | An introduction to modern nonparametric statistics |
| title_auth | An introduction to modern nonparametric statistics |
| title_exact_search | An introduction to modern nonparametric statistics |
| title_exact_search_txtP | An introduction to modern nonparametric statistics |
| title_full | An introduction to modern nonparametric statistics James J. Higgins |
| title_fullStr | An introduction to modern nonparametric statistics James J. Higgins |
| title_full_unstemmed | An introduction to modern nonparametric statistics James J. Higgins |
| title_short | An introduction to modern nonparametric statistics |
| title_sort | an introduction to modern nonparametric statistics |
| topic | Non-parametrische statistiek gtt Nonparametric statistics Nichtparametrische Statistik (DE-588)4226777-8 gnd |
| topic_facet | Non-parametrische statistiek Nonparametric statistics Nichtparametrische Statistik |
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