Multivariate Functional Data Analysis and Its Application to Growth Curves

Abstract Functional data are high dimensional data recorded continuously during a time interval at discrete time points. Statistical methods for analyzing functional data have been widely studied; however, dependent functional data that exhibit additional complex features such as time or contemporaneous dependence, stochastic volatility, jumps or rapid-changing smoothness, sparsely or irregular with non-negligible error is a challenge in existing methods. In this article, a proposed nonparametric approach to analyzing functional data that includes a variety of such complexities is used to analyze growth trajectories. The monthly weight of children registered and receiving immunization at Bishop Murray Medical Centre, Makurdi for a period of nine months was retrieved and used as training dataset to estimate change over time within each individual and then compare change across individuals. Exploratory analysis of the curve, mean, standard deviation and bivariate correlation functions were conducted. The principal component analysis reduced the multivariate data to a finite-dimensional vector of basis and visualizes the variation in the functional data. The least square regression model for fitting of basis expansions procedure was used for smoothing of the curve. The principal component curves and coefficient for the functional linear regression model and the functional parameters was estimated for the selected basis functions. Model adequacy was checked using root mean square error of approximation. The fitted model is significant as it provides the estimation of the principal components using functional regression.