Smoothing spline ANOVA for time-dependent spectral analysis
Smoothing spline ANOVA for time-dependent spectral analysis
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DOI：
10.1198/016214503000000549
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发表时间：
2003-09-01
影响因子：
3.7
通讯作者：
von Sachs, R
中科院分区：
文献类型：
--
作者：
Guo, WS;Dai, M;von Sachs, R
在本文中，我们提出了一种平滑样条方差分析模型（SS-ANOVA）来估计和推断局部平稳过程的时变对数谱。假设时变频谱在时间和频率上都是平滑的。这种假设本质上将时频谱估计问题转化为二维表面估计问题。使用平滑局部复指数 (SLEX) 基础来计算初始周期图，并将 SS-ANOVA 拟合到对数周期图。这种方法允许以统一的方法对时域和频域进行建模并联合估计。对于时变频谱，可以采用为 SS-ANOVA 提出的置信区间和假设检验等推理程序。由于基础频谱的平滑假设，一旦我们获得了时频网格的估计，我们就可以计算任何给定时间和频率的估计。这带来了很高的计算效率，因为对于大型数据集，我们只需要在更粗糙的网格上估计初始原始周期图。我们研究了惩罚最小二乘估计器和惩罚 Whittle 似然估计器。惩罚Whittle似然估计器均方误差较小，而基于惩罚最小二乘法的推理可以采用现有结果。我们展示模拟结果并将我们的方法应用于癫痫发作期间记录的脑电图数据。
In this article we propose a smoothing spline ANOVA model (SS-ANOVA) to estimate and to make inference on the time-varying logspectrum of a locally stationary process. The time-varying spectrum is assumed to be smooth in both time and frequency. This assumption essentially turns a time-frequency spectral estimation problem into a 2-dimensional surface estimation problem. A smooth localized complex exponential (SLEX) basis is used to calculate the initial periodograms, and a SS-ANOVA is fitted to the log-periodograms. This approach allows the time and frequency domains to be modeled in a unified approach and jointly estimated, Inference procedures, such as confidence intervals, and hypothesis tests proposed for the SS-ANOVA can be adopted for the time-varying spectrum. Because of the smoothness assumption of the underlying spectrum, once we have the estimates on a time-frequency grid, we can calculate the estimate at any given time and frequency. This leads to a high computational efficiency, because for large datasets we need only estimate the initial raw periodograms at a much coarser grid. We study a penalized least squares estimator and a penalized Whittle likelihood estimator. The penalized Whittle likelihood estimator has smaller mean squared errors, whereas inference based on the penalized least squares method can adopt existing results. We present simulation results and apply our method to electroencephalogram data recorded during an epileptic seizure.