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.
2. Models for Cross–Sectional Data.
3. Univariate U–Statistics.
4. Models for Clustered Data.
5. Multivariate U–Statistics.
6. Functional response Models.