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Enveloping spectral surfaces: covariate dependent spectral analysis of categorical time series
Journal of Time Series Analysis ( IF 1.2 ) Pub Date : 2012-01-19 , DOI: 10.1111/j.1467-9892.2011.00773.x
Robert T Krafty 1 , Shuangyan Xiong 1 , David S Stoffer 1 , Daniel J Buysse 2 , Martica Hall 2
Affiliation  

Motivated by problems in Sleep Medicine and Circadian Biology, we present a method for the analysis of cross-sectional categorical time series collected from multiple subjects where the effect of static continuous-valued covariates is of interest. Toward this goal, we extend the spectral envelope methodology for the frequency domain analysis of a single categorical process to cross-sectional categorical processes that are possibly covariate dependent. The analysis introduces an enveloping spectral surface for describing the association between the frequency domain properties of qualitative time series and covariates. The resulting surface offers an intuitively interpretable measure of association between covariates and a qualitative time series by finding the maximum possible conditional power at a given frequency from scalings of the qualitative time series conditional on the covariates. The optimal scalings that maximize the power provide scientific insight by identifying the aspects of the qualitative series which have the most pronounced periodic features at a given frequency conditional on the value of the covariates. To facilitate the assessment of the dependence of the enveloping spectral surface on the covariates, we include a theory for analyzing the partial derivatives of the surface. Our approach is entirely nonparametric, and we present estimation and asymptotics in the setting of local polynomial smoothing.

中文翻译:

包络谱面:分类时间序列的协变量相关谱分析

受睡眠医学和昼夜节律生物学问题的启发,我们提出了一种分析从多个主题收集的横断面分类时间序列的方法,其中静态连续值协变量的影响很重要。为了实现这一目标,我们将用于单个分类过程的频域分析的频谱包络方法扩展到可能依赖于协变量的横截面分类过程。该分析引入了一个包络谱面,用于描述定性时间序列的频域属性与协变量之间的关联。通过从以协变量为条件的定性时间序列的缩放,找到给定频率下的最大可能条件功率,所得表面提供了协变量和定性时间序列之间关联的直观可解释的度量。最大化功效的最佳缩放通过识别定性序列的方面提供科学洞察力,这些方面在给定频率下具有最明显的周期性特征,条件是协变量的值。为了便于评估包络光谱表面对协变量的依赖性,我们包含了一个用于分析表面偏导数的理论。我们的方法完全是非参数的,我们在局部多项式平滑的设置中呈现估计和渐近。最大化功效的最佳缩放通过识别定性序列的方面提供科学洞察力,这些方面在给定频率下具有最明显的周期性特征,条件是协变量的值。为了便于评估包络光谱表面对协变量的依赖性,我们包含了一个用于分析表面偏导数的理论。我们的方法完全是非参数的,我们在局部多项式平滑的设置中呈现估计和渐近。最大化功效的最佳缩放通过识别定性序列的方面提供科学洞察力,这些方面在给定频率下具有最明显的周期性特征,条件是协变量的值。为了便于评估包络光谱表面对协变量的依赖性,我们包含了一个用于分析表面偏导数的理论。我们的方法完全是非参数的,我们在局部多项式平滑的设置中呈现估计和渐近。为了便于评估包络光谱表面对协变量的依赖性,我们包含了一个用于分析表面偏导数的理论。我们的方法完全是非参数的,我们在局部多项式平滑的设置中呈现估计和渐近。为了便于评估包络光谱表面对协变量的依赖性,我们包含了一个用于分析表面偏导数的理论。我们的方法完全是非参数的,我们在局部多项式平滑的设置中呈现估计和渐近。
更新日期:2012-01-19
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