Template based functional prediction with applications to noninvasive mechanical ventilation and surface EMG techniques

Sample paths of physiological measurements often exhibit periodically similar patterns. The shapes of observed curves can be complicated, and between-subject variability is typically high. Modelling and prediction therefore need to be done at a patient-specific level. We consider models based on stationary warping of subject-specific template functions. The proposed models can be understood as state space processes or functional time series, with warping functions and vertical deviations characterized by real valued latent processes. Estimation, asymptotic results and prediction regions are derived. The methodology is motivated by a study of mechanical ventilation where the aim is to design automated noninvasive procedures for neurally derived regulation of mechanical ventilation, applying surface electromyography of the respiratory muscles.