具有组内谱变异的时间序列判别分析
Discriminant Analysis of Time Series in the Presence of Within-Group Spectral Variability
摘要：
许多研究记录来自不同组的重复时间序列时期，目的是使用频域特性来区分组。在许多应用中，同一组中的时间序列的周期模式存在变化。虽然已经探索了许多用于时间序列的判别分析的频域方法，但是缺乏考虑组内谱变异性的模型和方法。本文提出了一个模型组的时间序列，其中传递函数建模为随机变量，可以占两个组间和组内的差异，从个别重复的光谱。随后的判别分析随机倒谱在此模型下的开发，以获得最佳的组内光谱变异的存在下，分离组的相对功率的简约措施。该方法具有良好的属性，在新的观测分类，并可以通过一个简单的判别分析有限数量的估计倒谱系数的一致估计。在模拟研究中，并通过步态变异性的分析，说明了在考虑组内光谱变异性的经验。
英文摘要：
Many studies record replicated time series epochs from different groups with the goal of using frequency domain properties to discriminate between the groups. In many applications, there exists variation in cyclical patterns from time series in the same group. Although a number of frequency domain methods for the discriminant analysis of time series have been explored, there is a dearth of models and methods that account for within-group spectral variability. This article proposes a model for groups of time series in which transfer functions are modeled as stochastic variables that can account for both between-group and within-group differences in spectra that are identified from individual replicates. An ensuing discriminant analysis of stochastic cepstra under this model is developed to obtain parsimonious measures of relative power that optimally separate groups in the presence of within-group spectral variability. The approach possess favorable properties in classifying new observations and can be consistently estimated through a simple discriminant analysis of a finite number of estimated cepstral coefficients. Benefits in accounting for within-group spectral variability are empirically illustrated in a simulation study and through an analysis of gait variability.
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