Functional Spectral Analysis

• Activity Number: 406
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Robert Krafty*+ and Wensheng Guo and Martica Hall
• Companies: University of Pittsburgh and University of Pennsylvania and University of Pittsburgh
• Keywords: Spectral Analysis ; Time Series ; Functional Data

Abstract

In many experiments, time series data can be collected from multiple units and multiple time series segments can be collected from the same unit. In this talk, I discuss the mixed effects Cramer spectral representation which can be used to model the effects of design covariates on the second order power spectrum while accounting for potential correlations among the time series segments collected from the same unit. The transfer function is composed of a deterministic component to account for the population-average effects and a random component to account for the unit-specific deviations. The resulting log-spectrum has a functional mixed effects representation where both the fixed effects and random effects are functions in the frequency domain. A data driven iterative estimation procedure is offered for periodic smoothing spline estimation. The proposed methodology is used to investigate psychological stress in older adults who are the primary caregiver for their spouse via a spectral analysis of heart rate variability collected during a sleep study.