Multivariate U-statistics: a tutorial with applications
Article first published online: 10 JUN 2011
Copyright © 2011 John Wiley & Sons, Inc.
Wiley Interdisciplinary Reviews: Computational Statistics
Volume 3, Issue 5, pages 457–471, September/October 2011
How to Cite
Yu, Q., Tang, W., Kowalski, J. and Tu, X. M. (2011), Multivariate U-statistics: a tutorial with applications. WIREs Comp Stat, 3: 457–471. doi: 10.1002/wics.178
- Issue published online: 2 AUG 2011
- Article first published online: 10 JUN 2011
- generalized estimating equations;
- missing at random;
- regression analysis;
- social network model;
- variance homogeneity
U-statistics represent an important class of statistics arising from modeling quantities of interest defined by multi-subject responses such as the classic Mann–Whitney–Wilcoxon rank tests. However, classic applications of U-statistics are largely limited to univariate outcomes within a cross-sectional data setting. As longitudinal study designs become increasingly popular in today's research, it is imperative to generalize the classic theory of U-statistics to such a study setting to meet the challenges of modern clinical and translational research. In this article, we focus on applications of U-statistics to longitudinal study data. We first give a brief overview of U-statistics and then discuss how to apply this powerful class of statistics to model quantities of interest with a longitudinal data setting. In addition to generalizing U-statistics and associated inference theory to longitudinal data analysis, we also discuss a class of function response models (FRM) to bring the power of U-statistics to uncharted territory. We illustrate applications of generalized U-statistics and FRM with data from some real longitudinal studies. WIREs Comp Stat 2011 3 457–471 DOI: 10.1002/wics.178
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