An Accelerated-Time Model for Response Curves

We propose a nonparametric method of data analysis for situations where the data consist of a sample of curves and a covariate is present. We assume the observed curves to be time-accelerated versions of a basic underlying stochastic process and assume the time acceleration factor for each observed process, determining the “eigenzeit,” to be a smooth function of the covariate. We discuss an iterative procedure to estimate the components of the model nonparametrically, using cross-validation to determine smoothing parameters using a leave-one-curve-out technique. Our example concerns time courses of mortality for a sample of cohorts of fruit flies.