Nonparametric mixed effects models for unequally sampled noisy curves

We propose a method of analyzing collections of related curves in which the individual curves are modeled as spline functions with random coefficients . The method is applicable when the individual curves are sampled at variab le and irregularly spaced points. This produces a low-rank, low-frequency a pproximation to the covariance structure, which can be estimated naturally by the EM algorithm. Smooth curves for individual trajectories are construc ted as best linear unbiased predictor (BLUP) estimates, combining data from that individual and the entire collection. This framework leads naturally to methods for examining the effects of covariates on the shapes of the cur ves. We use model selection techniques-Akaike information criterion (AIC), Bayesian information criterion (BIC), and cross-validation - to select the number of breakpoints for the spline approximation. We believe that the met hodology we propose provides a simple, flexible, and computationally effici ent means of functional data analysis.