Statistica Sinica 23 (2013), 769-789

NONPARAMETRIC REGRESSION ANALYSIS OF

MULTIVARIATE LONGITUDINAL DATA

Dongdong Xiang$^{1}$, Peihua Qiu$^{2}$ and Xiaolong Pu$^{1}$

$^{1}$East China Normal University and $^{2}$University of Minnesota

Abstract: Multivariate longitudinal data are common in medical, industrial, and social science research. However, statistical analysis of such data in the current literature is restricted to linear or parametric modeling, which may well be inappropriate in applications. On the other hand, all existing nonparametric methods for analyzing longitudinal data are for univariate cases only. When longitudinal data are multivariate, nonparametric modeling becomes challenging, as one needs to properly handle the association among the observed data across different time points and across different components of the multivariate response. Motivated by data from the National Hearth Lung and Blood Institute, this paper proposes a nonparametric modeling approach for analyzing multivariate longitudinal data. Our method is based on multivariate local polynomial smoothing. Both theoretical and numerical results show that it is useful in various settings.

Key words and phrases: Cluster data, local polynomial regression, longitudinal data, multivariate regression.