Prediction of Remaining Lifetime Distribution from Functional Trajectories Based On Censored Observations
Abstract
The goal in functional data studies on failure time or on death time of the objects is to find a relationship between age-at-death (failure time) and current values of a functional predictors. In this study, a novel technique is applied to predict the failure time of devices (such as bearings in a mechanical system) and to try to predict the “age-at-death” distributions under censoring data. We concern ourselves with circumstances where all co-variate trajectories are observed until a current time t. The predictors observed up to current time can be shown by time-varying principal component scores which is continuously updated as time progresses. We establish the estimation of modified survival function for longitudinal trajectories by inspiring Kaplan-Meire method in order to predict mean residual life distribution. Projecting behavior of co-variate trajectories on single index we reduce their dimension to get predictions for each individual object. Furthermore, the uniform convergence rate is proved for mean and co-variance function for censored functional data based on some specified conditions. The proposed method is validated as the leave-one- out method and the approach is illustrated using the simulation study as well