A timely and applied approach to the newly discovered methods and
applications of U-statistics
Built 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 contemporary areas of study including
biomedical and psychosocial research. Utilizing a ‘learn by
example’ approach, this book provides an accessible, yet in-depth,
treatment of U-statistics, as well as addresses key concepts in
asymptotic theory by integrating translational and
cross-disciplinary research.
The authors begin with an introduction of the essential and
theoretical foundations of U-statistics such as the notion of
convergence in probability and distribution, basic convergence
results, stochastic Os, inference theory, generalized estimating
equations, as well as the definition and asymptotic 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
Parametric and distribution-free mixed-effect and structural
equation models
A new multi-response based regression framework for non-parametric
statistics such as the product moment correlation, Kendall’s tau,
and Mann-Whitney-Wilcoxon rank tests
A new class of U-statistic-based estimating equations (UBEE) for
dependent responses
Motivating examples, in-depth illustrations of statistical and
model-building concepts, and an extensive discussion of
longitudinal study designs strengthen the real-world utility and
comprehension of this book. An accompanying Web site features SAS?
and S-Plus? program codes, software applications, and additional
study data. Modern Applied U-Statistics accommodates second- and
third-year students of biostatistics at the graduate level and also
serves as an excellent self-study for practitioners in the fields
of bioinformatics and psychosocial research.
Table of Content
Preface.
1. Preliminaries.
2. Models for Cross-Sectional Data.
3. Univariate U-Statistics.
4. Models for Clustered Data.
5. Multivariate U-Statistics.
6. Functional response Models.
References.
Subject Index.
About the author
Jeanne Kowalski, Ph D, is Assistant Professor in the Division of
Oncology Biostatistics at The Johns Hopkins University. Dr.
Kowalski has authored or coauthored over thirty journal articles
that focus on a wide range of issues in medicine and public health
through the use of novel statistical methods, including
U-statistics, generalized linear mixed-effects models, generalized
estimating equations, asymptotics, and measurement error
models.
Xin M. Tu, Ph D, is Professor in the Department of Biostatistics
and Computational Biology as well as the Department of Psychiatry
at The University of Rochester in New York. Dr. Tu has authored or
coauthored over ninety publications in peer-reviewed journals
during his career and is acclaimed as one of the best-versed
authorities in the area of U-statistics.
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