Functional mixed effects spectral analysis

• 成果类型: Article
• 署名作者: Krafty, Robert T.; Hall, Martica; Guo, Wensheng
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; University of Pennsylvania
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asr032
• 发表日期: 2011
• 页码: 583598
• 关键词: Nonparametric regression; EFFECTS MODELS; spline models; covariance

摘要

In many experiments, time series data can be collected from multiple units and multiple time series segments can be collected from the same unit. This article introduces a 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. It is shown that, when the replicate-specific spectra are smooth, the log-periodograms converge to a functional mixed effects model. A data-driven iterative estimation procedure is offered for the periodic smoothing spline estimation of the fixed effects, penalized estimation of the functional covariance of the random effects, and unit-specific random effects prediction via the best linear unbiased predictor.