Modern applied U-statistics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley Pub.
2008
|
| Series: | Wiley series in probability and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xi, 378 p. |
| ISBN: | 9780471682271 0471682276 |
Staff View
MARC
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| 245 | 1 | 0 | |a Modern applied U-statistics |c Jeanne Kowalski ; Xin M. Tu |
| 264 | 1 | |a Hoboken, NJ |b Wiley Pub. |c 2008 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
їх
1
Preliminaries
1
1.1
Introduction
............................ 2
1.1.1
The Linear Regression Model
.............. 2
1.1.2
The Product-Moment Correlation
........... 5
1.1.3
The Rank-Based Mann-Whitney-Wilcoxon Test
... 7
1.2
Measurability and Measure Space
................ 9
1.2.1
Measurable Space
.................... 9
1.2.2
Measure Space
...................... 12
1.3
Measurable Function and Integration
.............. 14
1.3.1
Measurable Functions
.................. 15
1.3.2
Convergence of Sequence of Measurable Functions
. . 16
1.3.3
Integration of Measurable Functions
.......... 18
1.3.4
Integration of Sequences of Measurable Functions
. . . 21
1.4
Probability Space and Random Variables
........... 24
1.4.1
Probability Space
..................... 24
1.4.2
Random Variables
.................... 26
1.4.3
Random Vectors
..................... 27
1.5
Distribution Function and Expectation
............. 30
1.5.1
Distribution Function
.................. 30
1.5.2
Joint Distribution of Random Vectors
......... 33
1.5.3
Expectation
........................ 36
1.5.4
Conditional Expectation
................. 38
1.6
Convergence of Random Variables and Vectors
........ 41
1.6.1
Modes of Convergence
.................. 41
1.6.2
Convergence of Sequence of I.
I.D.
Random Variables
. 43
1.6.3
Rate of Convergence of Random Sequence
....... 44
1.6.4
Stochastic op(-) and Op
(■)................ 48
vi
CONTENTS
1.7
Convergence of Functions of Random Vectors
......... 50
1.7.1
Convergence of Functions of Random Variables
.... 50
1.7.2
Convergence of Functions of Random Vectors
..... 55
1.8
Exercises
............................. 58
2
Models for Cross-Sectional Data
63
2.1
Parametric Regression Models
.................. 64
2.1.1
Linear Regression Model
................. 65
2.1.2
Inference for Linear Models
............... 68
2.1.3
General Linear Hypothesis
............... 81
2.1.4
Generalized Linear Models
............... 87
2.1.5
Inference for Generalized Linear Models
........ 101
2.2
Distribution-Free (Semiparametric) Models
.......... 104
2.2.1
Distribution-Free Generalized Linear Models
..... 105
2.2.2
Inference for Generalized Linear Models
........ 107
2.3
Exercises
............................. 115
3
Univariate U-Statistics
119
3.1
U-Statistics and Associated Models
............... 120
3.1.1
One Sample U-Statistics
................. 121
3.1.2
Two-Sample and General
К
Sample U-Statistics
. . . 131
3.1.3
Representation of U-Statistic by Order Statistic
. . . . 137
3.1.4
Martingale Structure of U-Statistic
........... 144
3.2
Inference for U-Statistics
..................... 150
3.2.1
Projection of U-statistic
................. 152
3.2.2
Asymptotic Distribution of One-Group U-Statistic
. . 157
3.2.3
Asymptotic Distribution of K-Group U-Statistic
. . . 164
3.3
Exercises
............................. 170
4
Models for Clustered Data
175
4.1
Longitudinal versus Cross-Sectional Designs
......... 176
4.2
Parametric Models
........................ 179
4.2.1
Multivariate Normal Distribution Based Models
. . . 179
4.2.2
Linear Mixed-Effects Model
............... 184
4.2.3
Generalized Linear Mixed-Effects Models
....... 191
4.2.4
Maximum Likelihood Inference
............. 193
4.3
Distribution-Free Models
..................... 198
4.3.1
Distribution-Free Models for Longitudinal Data
.... 198
4.3.2
Inference for Distribution-Free Models
......... 201
4.4
Missing Data
........................... 209
CONTENTS
VU
4.4.1
Inference for Parametric Models
............ 211
4.4.2
Inference for Distribution-Free Models
......... 214
4.5
GEE II for Modeling Mean and Variance
............ 223
4.6
Structural Equations Models
.................. 230
4.6.1
Path Diagrams and Models
............... 230
4.6.2
Maximum Likelihood Inference
............. 237
4.6.3
GEE-Based Inference
.................. 241
4.7
Exercises
............................. 243
5
Multivariate U-Statistics
249
5.1
Models for Cross-Sectional Study Designs
........... 250
5.1.1
One Sample Multivariate U-Statistics
......... 250
5.1.2
General
К
Sample Multivariate U-Statistics
...... 273
5.2
Models for Longitudinal Study Designs
............. 279
5.2.1
Inference in the Absence of Missing Data
....... 280
5.2.2
Inference Under MCAR
................. 284
5.2.3
Inference Under MAR
.................. 294
5.3
Exercises
............................. 304
6
Functional Response Models
309
6.1
Limitations of Linear Response Models
............. 311
6.2
Models with Functional Responses
............... 316
6.2.1
Models for Group Comparisons
............. 317
6.2.2
Models for Regression Analysis
............. 326
6.3
Model Estimation
......................... 333
6.3.1
Inference for Models for Group Comparison
...... 335
6.3.2
Inference for Models for Regression Analysis
...... 347
6.4
Inference for Longitudinal Data
................. 352
6.4.1
Inference Under MCAR
................. 353
6.4.2
Inference Under MAR
.................. 360
6.5
Exercises
............................. 367
References
373
Subject Index
375
A timely and applied approach to the newly discovered
methods and applications of U-statistics
•p
uilt on years of collaborative research and academic experience, Modern Applied
U
-Statistics
successfully presents a thorough introduction to the theory of U-statistics using in-depth examples
and applications that address
contemporan-
areas of study including
biomedical
and
psychosocial
research.
Utilizili«; a
learn by example approach, this book provides an accessible, yet in-depth,
treatment
oí
U-Stabstics, as well as addresses key concepts in asymptotic theory by integrating
translational and
cross-discipłmart
research.
The authors begin with an introduction ot the eoential and theoretical foundations of U-statistics
such as the notion ot convergence in probability and distribution, basic convergence results,
stochastic Qs, inference theory, generalized estimating equations, as well as the definition and
a-vmptotic properties of U-statistics. With an emphasis on nonparametric applications when and
where applicable, the authors then build upon this established foundation in order to equip readers
with the knowledge needed to understand the modern-day extensions of U-statistics that are
explored in subsequent chapters. Additional topical coverage includes:
Longitudinal data modeling with missing data
Parametrii
and distribution-tree mixed-effect and structural equation models
J A new multi-response baaed regression framework tor non-parametric statistics such as the
product moment correlation. Kendall s
tau,
and Mann-Whitney-Wilcoxon rank tests
A new class
rt U
-statistic-based estimating equations (UBEE) tor dependent responses
Motivating examples, in-depth illustrations of statistical and model-building concepts, and an
extensive
discusión
Ы
longitudinal stud)
designi
strengthen the real-world utility and compre¬
hension
oí
this book. An accompanying Web Mte feature·-
SAS
and S-Plus1 program codes,
software applications, and additional study data. Modem Applied
U
-Statistics accommodates
second- and third-vear
-indem-
of biostatistics at the graduate level and also serves as an excel¬
lent -elf-study for practitioners in rhe field- ot biointormatics and
psychosocial
research.
h
Assistant Frotessor in the Division ot Oncology Biostanstics at
The Johns
Норкиъ
L
niversitv. I>.
Kowalski
has authored or coauthored over thirty journal articles
that focus
ι α
a iride
range or issues in medicine and public health through the use ot novel statisti¬
cal methods, including U—t.mstio. generalized linear mixed-effects models, generalized estimat¬
ing equations, asymptotics, and measurement error models.
i< Prok-si
r
in the Department of Biostatistics and Computational Biology
Ж
well as the Department
Ы
Psychiatrv at The University ot Rochester in New York. Dr.
Tu
has
authored or coauthored over ninety publications in peer-reviewed journals dining his career and
is acclaimed a- one or the best-versed authorities in the area ot U-statistics.
Subscribe to our free Statistics
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470-0-471-^227-1
90000
|
| any_adam_object | 1 |
| author | Kowalski, Jeanne Tu, Xin M. |
| author_facet | Kowalski, Jeanne Tu, Xin M. |
| author_role | aut aut |
| author_sort | Kowalski, Jeanne |
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| bvnumber | BV041184438 |
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| dewey-full | 519.52 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.52 |
| dewey-search | 519.52 |
| dewey-sort | 3519.52 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| institution | BVB |
| isbn | 9780471682271 0471682276 |
| language | English |
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| physical | xi, 378 p. |
| publishDate | 2008 |
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| series2 | Wiley series in probability and statistics |
| spelling | Kowalski, Jeanne Verfasser aut Modern applied U-statistics Jeanne Kowalski ; Xin M. Tu Hoboken, NJ Wiley Pub. 2008 xi, 378 p. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Includes bibliographical references and index U-statistics Mathematical statistics U-Statistik (DE-588)4754777-7 gnd rswk-swf U-Statistik (DE-588)4754777-7 s DE-604 Tu, Xin M. Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026159648&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026159648&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Kowalski, Jeanne Tu, Xin M. Modern applied U-statistics U-statistics Mathematical statistics U-Statistik (DE-588)4754777-7 gnd |
| subject_GND | (DE-588)4754777-7 |
| title | Modern applied U-statistics |
| title_auth | Modern applied U-statistics |
| title_exact_search | Modern applied U-statistics |
| title_full | Modern applied U-statistics Jeanne Kowalski ; Xin M. Tu |
| title_fullStr | Modern applied U-statistics Jeanne Kowalski ; Xin M. Tu |
| title_full_unstemmed | Modern applied U-statistics Jeanne Kowalski ; Xin M. Tu |
| title_short | Modern applied U-statistics |
| title_sort | modern applied u statistics |
| topic | U-statistics Mathematical statistics U-Statistik (DE-588)4754777-7 gnd |
| topic_facet | U-statistics Mathematical statistics U-Statistik |
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