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Modern Applied U-Statistics

Jeanne Kowalski, Xin M. Tu

ISBN: 978-0-471-68227-1 December 2007 378 Pages


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.

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.


Subject Index.

  • The level of accessibility and the variety of timely applications that demonstrate the utility and power of the hybrid inference paradigm are unique to this volume. 
  • The scope of applications of the U-Statistics theory is more broadly defined than seen in other books. Emphasis is placed on nonparametric applications when and where appropriate.
  • The large number of motivating examples and real study applications in genetics, sequencing data, cDNA, protein arrays, biomedical and psychological research, as well as the concrete steps needed to apply the theory to practical problems, serves to strengthen the utility and comprehension of the book.
  • The use of case studies throughout the book underscores the real-life nature of the content. 
  • The unusual inclusion of certain topics such as repeated measurements and clustered data make the book timely and modern. 
  • The appendix of the book and a soon-to-be posted .ftp site provide several computer codes for producing the results that are discussed in the book.